I play games at home or at work, so I am nearly always near a power supply. Batteries are fine, but have their problems - including getting everything in the N64 working as it should, battery life, weight, etc. I will retain the power in socket from the PSone supply for the casing of the N64p, so I can, if I want to, run everything off batteries (external) via the input.
I figured that as you can run everything (screen, fan, PSone screen, N64) off one powerful battery or set of batteries, at 7.5v, that it was worth trying to run everything off the mains 7.5v power adapter supply you get with the PSone screen. The power supply that comes with the N64 fills its case - it is big, heavy and thick - and outputs 10.98v and 3.4v (mine anyway) so needs to be stepped down on the larger line for the PSone screen (max 9v). Using the PSone power supply, it is 7.5v, so runs the PSone screen and the larger voltage N64 line (7.5v is fine, as others have posted), but needs a converter for the 3.3v line (which some say run fine v. 2.8v - 4v). We all have one of these power supplies doing nothing - everyone who has used a PSone screen for a mod anyway.
The car adapter works fine - gives just under 3v on load, which is enough. Only thing I can't test yet is that it outputs max of 1 amp, the N64 needs (from what I understand) from 0.8amp - 1.3amp on full load - so it might be that most games run fine, but maybe not the ones where the N64 has to work hard, like Donkey Kong 64. Does anyone have a list of the high performance games (eg DK64) which put the N64 under more strain than other titles please?
I have a dead mobo from my 1st attempt yesterday; fried the 3.3v line trying to use a step-down regulator which rose over 4v and fried the mobo, giving off smoke on the mobo! I can use this dead board to experiment with relocation of the cartridge slot and removing the expansion port. Really pleased I bought a special screwdriver off E-bay to take off the pesky N64 screws - saved me lots of time! Fortunately, N64's are easy to buy on E-bay and cheap, I paid about £14 for one, delivered, with 2 controllers and a few games!
The serial number of the N64 starts with NUP13....... which means, according to posts I read, I might be able to output in RGB mode (NUP17 or under you can, later models not apparently). Composite is ok, not great, so I want to make this RGB via the PSone screen. Time will tell!
Progress to date - ignore the rubbish on the desk!

Crude diagram below. Functional, not pretty....

Lots of work to do yet, and it may be a few days before I have a decent update (may have some minor ones in the meantime).