With 125k on it, I guess it's time, even though the coolant looks like new in the reservoir. Is it possible to run the engine while flushing in order to open the thermostat? This would eliminate the hassle of gasket scraping and replacement, re-installing the T-stat wrong, etc.

 

At 125k, why not replace the thermostat while you are at it?

But if you don't want to, yes you can flush with the stat in. I've done it many times.