First, given your circumstances if you cannot fix it quickly bite the bullet and get a plumber out to fix it. I will cost you but it will likely be quicker to figure out and fix compared to DIY'ing it.
I think I followed what you have done to date and I have to agree with the others that there is likely a larger problem here, such as old corroded pipes that are in need of replacement. I've never had to work with pipes that weren't copper/PVC/CPVC/PEX, but my suspicion is the pipes (specifically the hot pipe) have corroded and are now shedding and fouling the internals of the cartridge. That would explain why replacing the cartridge worked for a while and why things get hotter without the (stopped-up) cartridge. As to the water not being as hot as downstairs without the valve, no matter how good the pipes some amount of temperature drop is normal as distance increases, but corroded pipes with a reduced diameter could make it worse.
If it is, as the consensus appears to be, that the original pipe has reached end of life, the only real solution is to replumb. And if the upstairs bathroom hot has reached end of life ... well its likely so has the rest of the house (both hot and cold) or will soon. I suppose a short term solution could be to replace the cartridge, it has worked for a time before but it will likely happen again.
Can you take the aerator screens of some of the sinks in the house, including the one in the impacted bathroom, and see if there is similar debris caught in them?