Hi fellow Zonie Herdo, welcome.
I had a house for a decade on the Glendale/Phoenix border at 51st Ave and Cactus, I'm in Sunnyslope off of 15th Ave and Peoria now.
I really like that kit, I get mine from gasbike.net for about $20 less delivered than your link but it's the same 4G kit (maybe) my latest 4-stroke kit had a different left side cover and I like it better.
I am very worried about the law here in Arizona regarding motorized bicycles however. Apparently, anything over 48cc is illegal, and if caught going 20mph or more, your bike is then reclassified as a moped, which means you are looking at thousands of dollars in fines, not to mention having your bike impounded.
Technically the 49cc HS 4-stroke is 48.7cc so if you throw out the fraction it's 48cc and legal here.
I am coming up on 4 years of riding locally far over 20MPH one these things and well over 100 customers I have built them for with way more than legal size and the bottom line is if you ride safely the local police have far better things to do than hassle you about you bike and neither myself or any of customers have ever been hassled.
Heck I was on my high performance 66cc shifter doing 38 on 43rd ave at about Northern (40MPH speed limit) on the right side of the 3 lane south bond roadway and a cruiser with two cops came to pace me.
I looked over, smiled and nodded my head and they both just smiled, nodded and went on by.
I had on glasses, a bike helmet, and a front flashing light so not a danger to myself or others.
I've read a couple horror stories of people here in Phoenix having their bikes impounded, and never getting them out due to a lack of evidence of ownership (no VIN numbers or registration, etc).
I know of one, a kid that was not riding responsibly and that drew the cops attention.
As far as proof of ownership goes make yourself up a receipt like I give my customers.
Your name, serial numbers and a picture pretty much says it all, for 48cc bikes with the engine plate I include the AZ law printed on the back to whip out.
I found a forum member who was apparently looking to change the laws earlier this year, but it looks like the bill died so maybe next year something will happen.
That would be me, and I've been trying for 2 years and will try again next legislative session ;-}
I don't know what Schwinn model bike you are looking at but I've build 2 of these 4-strokers on that 29" Macargi Fatal Love bicycle for about $220 at the Try Me Bicycle Shop around the corner from me on 15th Ave and Hatcher and I love them, in fact they are the shop favorite and I have 3rd one sitting here waiting for me to drop in a 79cc Predator 4-stroke with a shifting Torque Converter transfer case, if anything will get a cops attention that will be it but again it is not about the machine you are operating, it is how you are operating it that gets the attention, I mean even going through a DUI checkpoint they simply just don't look at the machine.