Yeah I have two engines that do this, the latest to start this side to side mess is one of my dax engines, it's the one I actually ended up GPS'ing 52.0 mph out of on the old western flyer bike, I think I got it a little hot and trashed the temper in the rings because it lost power big time as if it had no compression, i pulled the jug and the cylinder bore and piston were both in good shape but the skirt on the piston is really oily black carboned up from the serious blow by from the lack of ring seal.
While I was looking at that issue I just happen to push the piston to the side and thats when I noticed the crank had all the side to side movement and I though, well this ain't good....!
I set that engine aside until I can take it down and see for sure what's going on, but i would imagine its just as you found with yours and the crank is just sliding in the bearings.
Maybe if I could find a brass bushing that had the right iD that was at least very close to the size if the shaft and not to thin, a fella could make a couple spacers for each side of crank between it and the bearing and resolve that problem.
I found out after it was a little late of the old BGF engine, I was on my way back from about a 10 mile ride, I was cruising smoothly at about 36 mph and all the sudden the engine had a slightly different sound, my first reaction was to let off the throttle, but much to my surprise when I released the throttle nothing happened,it's like I was stuck on cruise control, bike was just zipping right on down the road... I thought the carb slide had stuck wide open at first and just continued for maybe another mile or so, I reached down and even closed thr choke and it actually seemed to run a little better and thats when I knew what it was...HUGE air leak, long story short... I had to shut it down and peddle for about 5 miles up and down hills all the way home, and when I pulled the mag cover I saw aluminum shavings all in there, I pull the rotor and then seen where it had rubbed into the seal until it ruined it and there my HUGE air leak was.
Sad thing about all this was that this engine had just got to the point to where it was smoother running than ever and was such a pleasure to ride.
The case may actually be savable since it just barely shaved enough material until the rotor contacted the seal and ruined it, if I can save the case and reuse it that will be nice since it's a large from mount case and these sure work out nice on the cruiser frames.
That's the same exact reason I originally tore into my first engine... it had about 1/8" of crank walk and I just happened to notice it one day when I had the mag cover off, the crank moved really freely then felt like it was locked up, then next time I tried to move the crank I noticed it was moving side to side a lot.
I took that one all the way apart to get the crank out and everything looked just fine, the crank was sliding side to side on the bearings, they were ok too, just felt a little rough due to being so cheap. After I trued the crank I put the bottom end back together temporarily to see what things were like and saw where the play was. I was going to make a few washers to keep the crank centered but at the time i had a lot of other stuff going on so I bought a new Dax lower and put my top half onto, bought a new jug but decided the old jug had better looking ports, the new one was one with smaller transfers that were slanted across the top instead of straight, and the old one already had the transfers cleaned as well as everything else opened up really nice so it would take less time to just make the old jug work on the Dax lower, the old jug only had about 30 minutes of run time on it anyway so it was practically new anyway...
What I think was going on with that setup was maybe they were relying on the crank being a tight fit on the bearings to keep it centered or they machined the steps off the crank or it was missing the spacers or washers... or who knows what they were thinking, and I was surprised it ran so well like that...
Hopefully yours is the same way and you find nothing wrong but the crank walk and can make or get some spacers for it, and also, when I temp installed it again with the crank straight and true it slid side to side even more freely...