Hi tyc21ac,
If you can provide the frame number I can probably date the outboard for you.
I suspect that you may be experiencing more than one fault with the engine but, for now, we will concentrate on the stalling issue.
Since it starts and runs at high speed I doubt that the fuel pump is causing the problem but anything is possible.
It sounds more to me like it could be getting hot. Even though the impeller is new, it may still not be moving enough water at higher revs. I almost never recommend replacing just the impeller. Instead, Honda sells a complete water pump kit that should be used if there is ANY wear to the old one. It costs more than doing just the impeller but it ensures that the pump is good to go for at least 3 seasons or more.
But, in this case, I think that you may first need to focus on the thermostat. Since it's a used unit, I recommend replacing the thermostat right off rather than trying to test it. Chances are that the previous owner neglected replacement. Most people don't do a very good job of monitoring engine temperature and thermostats rarely ever get looked at. This is even more of an issue if the outboard was primarily operated in salt water.
You will know as soon as you take the Tstat cover off. A "salty" will typically have a white, powdery look to the engine metal and possibly obvious evidence of the passages being clogged as a result. Careful cleaning would then be in order to try and remove the mineral deposits without removing and damaging the aluminum of the engine casting.
Dosing the outboard with white vinegar solution by running it in a bucket or trashcan can help break down the deposits somewhat. Then brushing the areas that you can reach with a stainless steel bristle as well as very careful and MILD scraping can help too. But you have to be very cautious not to clean too aggressively because the minerals embed themselves in the metal and taking too much can be harmful. It boils down to you have to just settle for what you can safely remove.
With the thermostat out and the lower unit removed the passages can be "backflushed" to clear any debris that may have lodged in the passages using shop air and full home water pressure.
I'm assuming that this is a tiller steer since the remote would have warning lights and a buzzer and you didn't mention them.
Let me know what you think.