gkull I think the problem with the high flow Stant T-stat is that with your overdriven pump it is overcoming the stat and forcing it closed. Look at the design of the Robert-Shaw T-stat, the water flows through from the sides of the stat. This flow puts less force to close the stat.

Neal

 

Wade the WP bypass at the top of the WP is there for higher RPM motors and is to eliminate water pump cavitation at high rpm.
On stock SB SHP motors on C2's such as the L79 350hp and L76 365hp this was standard but not on the lower HP SB motors because they had lower RPM redlines. ALL SB motors also have a bypass circuit thru the passenger side leg of the water pump
It was also standard on all BB motors since none of the BB pumps/blocks have the bypass hole in the passenger side leg like the SB motors do.

Disclaimer: this info is based on the C2 ( and '68 327 SB cars) cars with the 327 blocks. I'm not sure if the block and water passages and waterpumps were different on the 350ci blocks in the C3's to make this invalid for your question.
It's been while since I've looked at a C3 LT1 motor but if the same design holds than the LT1 would have the bypass hose on it and the lower HP SB's won't.

In regards to your question, on a higher RPM motor, if the coolant starts to cavitate than it's not flowing thru the system as efficiently as it should therefore not cooling as well as it should. I'd leave the bypass in place.
To be fair, I've never tried to A/B test a car with and without the bypass though to see how much of a difference it truely makes.

Also, gkull has an excellent point about your WP. Check the flow specs on it at normal driving RPM ranges. If it's designed as a race pump than it very well may not flow enough at the RPM's you are driving the car at. If that's the case than you are probably best off going back to a stock waterpump. Don't understimate the stock waterpumps - they flow well, have more than enough capacity, and are very reliable.