To answer your question I have an old ATR radiator boxing kit. I would have to confirm but it seals up very well. I don't have the horizontal plastic piece though that goes from grille to radiator and I feel the air goes to the intercooler scoop right below it once it hits the radiator.
IIRC taking off the rear hood weather stripping doesn't really help. Something about it being a high pressure area at speed. Plus half of it protects the AC from sucking up hot engine air.
If your temps are skyrocketing from having some openings in the box kit I think you have another issue or you have a very crappy box kit. All the air should go into the engine compartment after it goes through the radiator, and then under the car.
I agree, radiator, water pump, thermostat, relay, fan clutch could be any one of those things. Is it an old rad original? Mine was original and the fins were litterally crumbling out of it. As In-efficient as could possibly be.. my car is a Hot, hot-air. Now I have no problems, before the new W/P, and Radiator overheating would happen very quickly.
This was my process of elimination,
1-top up fluid
2-make sure your w/p is pumping.
3-check your thermostat is functioning or just replace it. 160°
4-check the fins on your rad for corrosion, and make sure there are no blockages.
5-make sure your fan clutch is working, it should feel smooth resistance when turning cold by hand.
5a-if your electric, then check your grounds, connections, relays.
I hope that helps.