In regards to warmth - couldn't feel any heat from them after over 20 mins running (although the diodes are protected with a layer of insulating tape and shrink tubing. No problems.
Testing system again, with a different (fresh) set of cells. 12 mins so far and going fine. Will let you know how everything goes.
Completely accept my electronics knowledge is basic and not up to many on this forum; I tend to experiment and test theories out. If one method fails, I try something else.
Here's the thing - wired up the traces from a GB cart and connected my wire from one end of the GB cart to the other (to turn system on automatically when cart is inserted), using the diodes:
* PSone screen is running perfectly.
* Plug'n'play is powered (red light is on).
* Plug'n'play is running perfectly on the PSone screen.
* Keeping check on diodes (they are enclosed in shrink tubing and in place by electrical tape) - can't feel any heat.
System is working perfectly, although I must have a dodgy wire somewhere as i'm not getting any audio at the moment (controls and d-pad work great though).
Can't turn system over to take pics at this stage as it is in bits, but take my word for the fact the demo screens on 1942, Ghosts and Goblins and Commando are going round in a loop at the moment!
I will keep the system on until it dies, then I know how long the batteries last for - I can then see why the audio isn't working ok (sure it is an easy fix).
My methods are unconventional, I know, but hey, if it works, that is what matters!!

Obviously the plug'n'play will be made into a small (ish) cart, this is just a test run. The excess cart slot on the plug'n'play isn't needed (apparently also gives you MegaMan as a fourth game if you have a cart to go into it, which I don't. That cart will be removed, some of the grounding removed, maybe relocate some of the capacitors, etc.
When this test is finished, I will rig up a couple more plug'n'plays before I take my work as "successful".
Update - over the 25 mins from attempt one with the shorted battery; going strong....
Two more pics - supporting system on a couple of SNES cart boxes so I can see under the system to check the screen is fine, without moving the system - the pic of the screen is bad, always is when you take a pic from a large angle (the screen is best looking squarer on, this is just to prove the system works for any unbelievers out there!):





