My wife's Giant Suede has a single chainring and 7 speed freewheel. It will sometimes lose the chain off the chainring when in lower gears, fortunately the plastic guards on the chainring keep it from falling off completely and it can be nudged back into place. I was eyeballing the chainline and it's straight in the 2nd smallest cog, with the largest cogs pulling the chain at a decent angle.

Can I reduce the chainline by swapping in a different bottom bracket with a shorter axle? I think if the chainline was straight around the middle of the cogs it would be less likely to drop the chain. It has a 4-arm JIS taper crank installed. Actually that crank is massive and no doubt extremely heavy. Is it better to just seek out a lighter crankset, a chainring with fresh teeth, and start from there?

on my 1x7's i try to cheat a little by lining up my chainring with the third largest cog. sometimes i can accomplish this by simply mounting the chainring on the inside of the spider if possible. but on cranks designed for only one chainring i suppose a narrower spindle should work. beware, there are limits to this. you'll know you reached the limit when either the crank's spider hits the driveside chainstay or the chainring does. solutions then would involve either a new type of crank (less dish to the spider) or a smaller chainring.

A dog fang chain keeper does a lot to keep a chain on a 7-speed single ring drivetrain.

The 7-speed Suede doesn't have a derailleur post, unfortunately.