There is really no place for the gear oil to leak out of that you cannot see. It's not like an engine and oil where the engine can burn oil.
I would just keep adding oil until it comes out of the vent.
I do not think running with the drive up and a thump are connected.
Running in shallow water can cause the outdrive to suck up muck or mud and if the props hit something it can damage the props and/or the outdrive. That can get expensive.
Pulling the outdrive is not a huge deal but a duoprop...
I feel for you with that engine hatch. On my Chaparral I have full access to everything with the engine hatch up. I can sit next to the engine down in the engine area. And I often do.
You can pull the old pump. Then pull the seal and look and see if the shaft is worn where the shaft seal seals the pump. If there is no grove then just replace the seal being careful not to tear it.
Also check the bearing. The shaft should turn smoothly without any stiffness or bearing noise.
Lower temp thermostat is for a RWC cooled engine running in salt water typically.
The raw water pump has an O-ring. That needs to be on good shape.
The raw water pump has a shaft seal and a bearing. The shaft seal is pretty easy to replace but the bearing needs a bearing puller, and an...
While I have never run into it, there have been cases where the vanes of the raw water impeller have broken off and got jammed in cooling passages.
People have also plumbed in a short section of clear tubing to watch water flow and or air bubbles.
I would look around at local boat launches and see what people have. Around salt water in Delaware it's mostly outboard. Hard to find people who will work on I/O.
I think rivers and lakes maybe be a slightly different story with a highed percentage of I/O and inboards.
The new 4 cycle...
Just thought I would provide this information on the Vetus joysticks for the Vetus bow thruster. Since I had to work through it.
If you have a several years old Vetus joystick the gray wire from the joystick provides +12V when the joystick is "turned on". The gray wire may or may not be used...