10 Amps is not the issue. The issue is it doesn’t put out ANY amps until it is running at somewhere around 2000 RPM. So, I suppose it might be possible to rev it up and slam it into gear. On the other hand, if the battery isn’t completely dead, it should put out enough to shift, even if not enough to run the starter. In any case, time to head for home.

You show some knowledge there. The generator retains some magnetism in the fields (polarization) to begin producing electricity as soon as it is spinning fast enough. No additional polarization is needed unless it has been sitting forever or has been messed with. DO NOT attempt to polarize the regulator on this system.

The problem here is that you have to rev up the engine before the generator kicks in, but you should only shift the engine at idle…And, if it did go into gear, you would not want to rev it up much because it might jump out of gear due to higher load on the system and extremely weak battery….Jumping out of gear at a higher RPM usually will cause internal damage to the electric shift gearcase….
So, I am thinking that a small spare battery would be the best solution to this scenario…But, you wouldn’t want to use regular jumper cables between the batteries, I would probably just connect the smaller battery to the engine and rope start it….Charge the normal battery properly when you get back home.
These engines usually have an ammeter, but that is not a great indicator of battery condition, just says the generator is putting out….You might consider adding a voltmeter in the dash (or perhaps underneath if you don’t want to mess up the boat’s dash board}.