Cooling issues seem to be one of the most frequent problems with boat engines, particularly sterndrives (I/O). Since the boat is new-2-you, you should go through the cooling system, which it sounds like you have done some.
If the new impeller did not fix the issue, then the overheating may be due to a clog in the water flow. How did the old impeller look? 100% intact?
Marine life and even bits from a failed impeller can clog the water flow before it gets to the engine or exhaust. Back-flushing and checking the various oil coolers along the water flow can remedy clogs.
Also, as mentioned, the exhaust system and thermostat housing can become clogged with rust scale, particularly when used in salt water. The cooling water exits the engine through the exhaust manifolds and/or risers (depending on which cooling system you have). If those things are clogged, not enough 'hot' water cannot exit the engine, so not enough 'cool' water from the ocean can enter.
I've run all 3 of my powerboats over the past 20 years in salt water and all of them had cooling issues at one point or another.