first question
what brand of stat are you running and what temp is it rated for? I have had lots of problems with aftermarket stats not functioning like they should or completely failing. I only use AC/DELCO stats now (or dealer for other branded vehicles)
second question.
when you filled the engine with coolant did you run it afterward and check to see if the stat opened and the rad level was topped off after? then, when the unit is cold again, pull the rad cap and check the level IN THE RAD, NOT THE OVERFLOW TANK?
third question.
have you checked your rad cap to ensure it is for the system type you are running. a system with no overflow would have only a single gasket/rubber on the end of the cap. a cap for use with the overflow tank would have that seal on the end plus a gasket right under the cap top to seal the cap with the top edge of the rad filler neck. the rad cap will likely be rated for 15-16 lbs and is an item that would be on just about any shops inspection list to be checked for seal integrity and also would need to pass a pressure test of the cap to see if it seals and relieves at the correct pressure. a check of the integrity of the rad cap seal, gasket and the sealing surfaces on the rad can reveal problems. the seal on the end of the rad cap should be flat and smooth, not cone shaped with a wear groove. the gasket under the cap should also be smooth with no wear groove. the overflow hose should be attached with a clamp to the spigot on the rad filler. the hose should draw fluid from near the bottom of the overflow tank and the overflow tank cap hose connection, if applicable, should also seal the hose properly.
fourth question.
you say the rad burped back into the overflow when you removed the cap. when it cooled off did you check to see if the overflow tank was back down where it should be? the system is made to burp out when heated and pressurized to the rad cap spec, then when it cools off it should also draw the fluid back into the system when the coolant contacts back to the same volume as it was before it heated and expanded. checking the coolant in the rad on a cold engine can tell you whether or not the system is full, completely, and whether or not the rad cap is allowing coolant to return to the engine when the engine cols off. simply checking the overflow tank level is not sufficient especially on a new system that you have not run before and gotten used to where the system levels find themselves working.
fifth question.
how does the relationship between the engine and the rad look? on some vehicles the rad has been lowered to fit the vehicle configuration and the air has a hard time finding it's way out since the t stat housing is almost higher than the rad cap. some cars even have a bleeder screw on the engine to bleed air out due to this problem.
sixth question.
are you sure your water pump is made to turn the direction it is turning? some were made for serpentine belt systems which turned backwards.
here is a blurb on t stat bleed holes and engine temps. made for the newer engines with computer control but shows where how and why to drill a hole in the stat. there are also stats available with the jiggle valve installed to allow air to escape and a small amount of flow. anyway, the important thing is to locate the hole at the top of the stat if the stat sits sideways/vertically in the engine. if it sits horizontally it shouldn't matter too much.
https://www.jerrysgaskets.com/thermo...-modification/
it seems to me, by your description of you "getting hot" issue, that there was air trapped in the engine so the stat wasn't seeing correct engine temp. in this scenario the temp gauge may also be reading incorrectly due to air entrainment or bubbles. since you got flow when the cap was removed it seems the bubbles found their way out. my concern would be the possibility that the stat is hanging up or not reliably opening. a new stat is cheap insurance especially if you plan to dig it out and drill a bypass hole. I would start with a reliable new stat first. check to ensure the system has a good chance of working properly, as far as coolant flow and availability of air to escape, then go from there. use antifreeze as well, not just water. antifreeze has some anti rust additives as well as additives to make the coolant absorb heat better than straight water and also stay liquid longer, both cold AND hot.
here is a pic (I think) of a stat housing with a bleeder screw. (if it attaches). it is from a chevy diesel. maybe something like this would help you bleed air from your system.
https://www.dieselhub.com/img/tutori...leed-valve.JPG
anyway, hope you get it figured out before something bad happens. keep us posted.