"How about running without a thermostat?"
That is not what you want to do. Specifically nixed by the FSM... I have posted pictures of the thermostat configuration in the past.....search will bring it up....
I think you need to consider pulling the core plugs ( freeze plugs) and block heater plug...and the drain plug.... and using a 90 degree head on a high pressure sprayer to knock loose and evacuate any rust or grime which has accumulated in the water cavities of the block. You will probably need to make and use a shop vac to help evacuate the stuff... the drain hole is too small....and would restrict the stuff so it would precipatate out before draining with the water through that small hole.
In the old days when an engine was rebuilt it was standard procedure to take the block to a vat and get it boiled out... then start up putting it back together.... I think too many times partial rebuilds are done to our engines due to lots of factors...and then at some point the accumulation of gunk in the water passages makes them ultra sensitive to extra heat load.
The Factory Shop manual specifies boiling out the block in a rebuild.... but many people don't read the FSM....