Can you be sure the t-stat is opening consistantly? An issue with parts store t-stats is that they can suffer from hysteresis. This can drive you nuts. The only ones I put trust in are the performance variants that are balanced. The ones I use are Mr Gasket. I recall you have a parts store connection (I think). Your pops should be able to order you one. It's a solid investment (10-12 bucks). In my personal testing, I had a cooling system up to par. I had a brand new parts store 180*F stat. I ran this for a week and swapped it for a Mr Gasket 180*F stat. My operating temps dropped about 7*F across the board. The Mr G flows better sooner and again, is balanced (that's real big).
Now the cap: Here's the deal with pressurizing the cooling system. Each PSI in the system raises the effective boiling point ~3*F. A 16 PSI cap raises the boiling point 48*F. Water at 1 ATM would boil in the range of temps you're seeing. It's pressurizing the system that keeps things in check. A bad cap can keep you from achieving full pressure (or any pressure). That's why this is so important.
If you have a cooling system pressure tester, toss it on your radiator and see how the system holds pressure. You can check your cap with them too (though I dont trust the cap test as much personally. If I have doubts, I replace the cap).
Now I never like throwing parts at things but if you're going to keep the car, I see a new radiator as a wise investment. I'd go with a 3 core HD unit (from parts stores under the GDI [Go-Dan-Industries] or Modine name). Or get an alum radiator (universal, from speed shops like Summit) and do a little fabbing and make it work. I will say that I have NOT installed a universal alum radiator with a stock fan, so I cannot comment about how that works.
Does any of this sound decent? I'm sure others will have other ideas as well.
Good luck Nick.
BTW, it could be worse. It was 102*F here today.