According to CARS Inc. catalog (oldbuickparts.com), 37 - 39 use an RC-10 non pressurized cap. The overheating may be caused by sludge (rust, scale, etc.) in the block, generally near the rearmost cylinders. This can be cleaned by flushing, but the best way is to remove the rear freeze plug and to get the sediment out. On my 47 248, I too did the fill it up and see how fast the water runs out 'gravity' test, which I thought went well, but I went and had a new radiator core done and it solved the problem. If you record the radiator, be sure to put a coolant filter (Google 'gano filter' ) in the upper radiator hose, to keep any remaining block sediment from moving into the new core and ruining it.
There are numerous threads on this forum that cover this topic of overheating and sediment in the Buick 8.
Good luck!
Jack