I have to agree with Tom, you don't want anything that locks you throttle.
If it is vibration that is getting to you, replace the hard plastic grips. Heck I do that to every build.
Before you drill anything out, please show some close up clear pictures of the carb throttle assy.
I have a similar Briggs 8000 and 9000 series engines and have changed the carb that came with them as they were not used from gravity feed gas tank. The bowl with float valves in the carb kind of carb I am talking about.
I had modified the carb but only slightly to get it to have a twist grip throttle. I also am off roading so I use gloves and the additional grip that is on the handle I know is tough on bare hands, but splash with mud and you have a better chance with this type.
Back to the point, I have many documentations on my motorbike carb throttle setup in the threads I have started.
I did not like the plastic part of my carb that the connection would be made to, in fear that it would soon break. I also did not have any easy way to continue to have a governor on my engine. The reason is that I had to use and elbow manifold to clear the frame. I added a spring, separate from the throttle cable return spring. The spring is just connected to the butterfly valve plastic part outside of the carb. It is connected to the twist grip throttle assy by means of a pin on the assembly that connects to the spring.
With this modification when I am at idle or at full throttle, the spring bends. This way there is only very small force that can be applied to that crummy plastic part on the carb.
When I had another carb temporarily being used it had it 180 degrees the opposite side I needed to have the cable going to the carb. I reused without changing any existing parts, just added some new parts and removed others. The end result was the carb had other issues I did not like and returned it for warranty refund. I still had the parts saved and reverted back to what I originally had.
All in all you I know are creative and have something going that I like in that bike build.
A twist grip throttle not using any lock is a good way to go. There are those that use other means by small levers and the like to have a throttle, but they I have most notice have a return spring and do not lock.
Above link to picture shows where the pin connects to inside the vertical spring. That vertical spring is connected under a block of aluminum on a pivot point. The pivot point is actually from a door hinge. I added a place to connect a twist grip throttle cable and return spring. Also adjustment stops limiting both idle and full throttle.
Just figured I'd also mention that there is a block of aluminum I drilled and made to put between the manifold elbow and the carb since the engine is on a tilt and this levels out the carb bowl and float to be at its best.
80302 I know it, manuals don't do nothing but I already found a tuning procedure long time ago, it's the cosmetics which are a considered.I guess this is an engine that has a centrifugal force weights inside the crankcase to operate the governor through a linkage outside the case. Not a fly wheel fins and and air vane type.
Also the connections seem to be hidden behind the carb picture where the idle screw with spring is shown.
It would seem then that the butterfly valve has a connection to an armature on two sides. The one side showing with the idle screw and the other side where it is connected to the governor and of course the cable that you adjust the throttle..
If you know the model number and make of the carb that would help, this given I do not know what this carb looks like hooked up in entirety. Even better if you know where a link for a pdf file for the carb exist, but I could try looking it up my self knowing make and model carb.
I do have a generator that uses a mechanical crankcase fly weight governor. It does not have a idle adjustment as it is meant to operate at a single speed only.
I don't know what the engine model you have. That would also be necessary as the linkage connection and a pictorial view of how it operates. I would hope the engine with that carb and governor was meant for operating at a range of speed.
Since you got it hooked up some how to run the bike from start to speed, I would think that it may have been used with that same stiff lawn mower adjustable speed throttle.
Maybe some one else already has done this kind of hook up on that same engine and carb. See what you can come up with on the specs so I can better help.
I don't think you should take apart the carb from the engine to get pictures as a lot of stuff is shown on save information on the internet. A good one I use is Smokstak.com
Above for detail pictorial diagrams shown of the 80300 series. It is air vane type governor.
Above check out this round throttle linkage. Not sure how it was attached, maybe press fit?
It could be used with some bracket attached some where on the engine to have it connect up. Not sure where the idle adjust went to since I thought it was mounted the same place on the carb.
You've helped enough and exactly as you have explained the setup is how I feel the vane is attached to the carb and is tensioned through the round nut located between the intake and air filter housing.Maybe the carb in conjuction with the governor on that engine was set up not to have a very slow idle. I guess I never used one of those types. The vacu-jet Briggs carb with air-vane governor I have had almost sound like a hit an miss idle without stalling very slow speed
I wonder if all the parts of the carb linkages with the governor are present.
What I remember is that the throttle cable is not hooked up to the butterfly valve directly.
The butter fly valve does have that idle adjust screw, but the throttle cable I remember going to another hinge plate of metal that connects to the air vane through a stiff wire linkage. That hinge plate is not the same as the butterfly valve.
When connected this way there is no struggling between a throttle cable and the governor.
The way it reacts as I remember on a lawn mower is that at idle it is kept from stalling.
Secondly when at say half full throttle going through a lawn of medium high growth, and then say you come upon much taller lawn the engine will slow temporarily.
Very soon afterwards the governor reacts since the fins on the slowing flywheel don't push the air-vane as much, the spring the becomes shorter. The shorter spring then move this hinge plate which is connected to the butterfly and thus compensates and speed the engine back up.
It will usually over compensate by a bit and speeds up too much just for a second.
Then it quivers a bit slowing and speeding up and slowing a few times and settles in at very close at the same speed of half full throttle as prior to encountering a thicker lawn to deal with.
You might become a member on that Smokstak.com and post the question there.
Maybe also find on this site some other place to ask the question rather than general discussion area.
Maybe try this area. Search first and maybe find an answer. Maybe also include Briggs in the search. Post question there if nothing help, but maybe that more defined area could turn up something.
If the spring is deformed it will impact how well it can idle since the governor is not operating as it should. Since I swapped to a carb that did not have a low and high speed fuel mixture screw, it has nothing adjustable, I do pulse the throttle a little to idle. The elbow manifold makes it that I had to do away with the governor.
One thing though is if the idle gets going too fast and you have to be not moving, you have to be quick with the kill switch button. Some times I have just held the brake, but the clutch shoes and drum can heat up adversely.
Have you come up with or gotten to what you were mentioning about making stronger or more rigid engine mount? Also maybe also adding an idler or back idler pulley for adjusting belt tension as it wears. Used a back idler pulley I made from some kind of nylon plastic with metal mount and bearings. Now that I just have one belt and two chains, the single belt is adjusted with an adjustable diameter pulley.