First you did not say what drive you have but since you said you changed the drive impeller it must be an Alpha.
Try removing the hose at the t-stat housing that comes from the transom assembly, should be the large hose on the port side. Start the engine to see if water is pumping out. If you have flow the impeller in the drive is working.
Only one impeller but the is a circulating water pump on the engine. Yes it could be the t-stat or clogged exhaust manifolds or elbows.
I would use a IR temp sensor and measure the t-stat housing and exhaust to see what everything is running at.
1997 2400 SCR
5.7 Vortec / Bravo 2