...so I have to have a fan facing directly behind my PS3...
Not a good idea. The rear ventilation ports blow out air, and forcing air into the vent would be going against the PS3's internal cooling system. You are literally having two fans fighting each other, leaving hot air trapped inside.
I would also internally clean the system, replace thermal pastes, that sort of stuff.
Also, HDMI and AV cables can be replaced. Try doing that before sinking money for a new PS3.
Replacing thermal worked for me. Ive had my ps3 60 since launch, thats about what? 7 years? Thats a very long time for 1 system to be played on. I put alot of hours on it. I saw alot of threads few years back about ps3 dying and what not, of course i just shrugged it off, but i did notice over past year playing bf3 quite a bit, the fans would always skip to high, and quite a bit of heat was coming out.
Main reason i didnt want to replace thermal paste is i was afraid to destroy the ps3, with leftover parts or screws. I found a video on youtube that made it quite easy. Bought some artic mx4 and tried it out. When i got to the CPU and GPU i was amazed how dried up the paste was. I knew it was a very long time but still was shocked.
After everything was said and done, i havent heard to ps3 fan yet on full speed. Even after 4 or 5 hours steady. I also want to point out, the only reason i decided to fix it now, is for gta 5 : ) last game to be bought on ps3.