Okay folks, though I said I'd update properly later on, I figured that I should at least give a small update in the meantime.
I've found myself a CPU for a decent price, more than I initially was planning to pay, but it should hopefully at least keep me going until I can afford to get the i7-4790K I want! The CPU is an i5-4670K, and it comes boxed and with the cooler, so for 90 quid I'm more than happy for the price! It's probably past the midway point for my CPU in some respects, but I realised that I probably need a CPU that I can overclock in case I need to squeeze out extra power later, but I do probably need to think about working case fans as well before I start doing that.
I do however hope that under load and clocked at normal, there should be less stress on the CPU in theory; the Linux browser plugin on OBS is quite CPU intensive, and although I set all my overlays back up, they're still consuming a lot of CPU, so, therefore, that plugin is the issue. I will be trying to reduce the CPU usage via that plugin, although I might have to accept that I can only do so much in that area. In any case, I can say that I'm making progress, although I am now also finding out that there's a "Global Source" option in OBS, so perhaps that might help things a bit!
Either way, I still at least have more I can do before the new CPU arrives, but hopefully I can reduce some more strain, as I do need to free up some CPU for running more demanding games as well!
Edit: It seems that in OBS Studio, all sources are global, so unfortunately that's a bust!