Find someone that can hook a gauge up to it or buy one. I think I have an "oil pressure gauge" that'd get the job done I got at HF cheap. You'll need one for at least 250 PSI.
The other thing to do is check your TV cable and make sure it's not outa wack as it controls line pressure.
It wouldn't surprise me if the 2nd gear bog is expected as well, 700R4s have a steep 1-2 ratio. If you're running it cold the fluid would have a higher viscosity and in turn that would tighten the converter increasing the RPM drop. It may be more noticable if you have some cam and a stock(ish) converter in it too IMO. The tighter the converter the more it will act like a manual (where the ratios directly determine the RPM drop at the shift)
Do you have a tach on it? Ultimately it's better to quantify these sort of things.
The other thing is it doesn't really stall does it? If it does, wondering about the lock up. Oh yeah, one more thing it's a late model gear box right? If it's 85 or earlier you WILL burn it up if you don't engage the torque converter clutch at cruise. Just warning you. Think the shift kit will correct it however.
Lastly it's plausible the ECU, mazes of vacuum line (if carb) and/or the TPI system was providing a more ideal mix at cold conditions and your carb is well fat as fuck when it's cold and you hit the accel enrichment. Ultimately the question in my mind is what change did you make when this started. The more changes you made at once, the more difficult it is to figure out.
ED:last thing to remember is that you're talking about an intake "rated" to 5800 on a 350. Most people don't rate on a 305. Because of that it's highly likely that intake is going to be fine for your 305 for higher than 5800, plausibly significantly higher. What is it exactly, a Performer or similar?