As far as the water pump is concerned, I've replaced one, it is not too bad of a job. It is just a little tight working on the front of the engine there. The pumps are cheap and plentiful. I have run one of my Volvos a long time without any thermostat, and it ran fine. But I live in California where we have mild winters. Since you live in the Big Apple you would be fine all summer without one, but come winter you will be running too cold. If you look around hard enough you can find thermostats with different temp settings. I bought one that was one step lower than stock (sorry, I don't remember the temp).
Of course, your concern of running hot is based on the Volvo temperature guage. Who knows how accurate it is? Since your fan is controlled by its own thermostat, it also helps control the water temp. If your temp guage says hot and your fan is not running, you should be ok, if your fan is set at proper temperature. But if the fan comes on and continues to run for a long time, then I would suspect the water pump.
On the other hand, the fan's sensor is in the top hose area and measures water coming through the thermostat. If the thermostat is not opening properly you could end up with hot water in the engine and cool water in the radiator and the fan will be off.
So, I would check the thermostat first, but since you improve things by increasing RPMs, I suspect it is the water pump. Water pumps are one of the few areas on Volvos that go out often.
Tom