Constant reload of CH34xx driver

Steve-SFX:
Hello

I am doing all of the above.

Except posting a schematic showing how you have wired up the Pro Mini and the Uno.

Steve-SFX:
I got the USBasp to work on the 5v Mini-Pro's, but you can't use the serial monitor with them.

That's correct. The USBASP is just a programmer, it doesn't have a USB-Serial function.
On that topic, if you've used the USBADP to program the Pro Mini then it will have removed the bootloader from the Pro Mini, and so you won't be able to use Serial to upload anyway.