Well I dont have the problem with pressure, mine is more in the sense of it not really doing any "cleaning". It just puts foam on the car and that is it. Maybe my idea on how it works might be wrong, but I was under the impression it broke down most of the dirt and made washing easier. Ive tried all five different settings on the gun.
Personally I do think the foam gun helps clean. Most of what it takes off for me is particulate matter and IMHO this is what a foam gun is good for. All those tiny bits of dust, fallout and grit that is stuck to the car is what causes swirls in the wash stage. I find that some pressure helps blast away the emulsified particles after foaming.
I have heard people using various methods when foaming but here is what I do and why.
1) Clean the wheels, I clean wheels first because it takes the longest and I don't want water drying on the car while I am doing wheels. They are also the dirtiest so I like to get rid of all that nastiness and change the water in my wash buckets before proceeding to the bodywork.
2) Foam the dry car, once the foam hits the car it will start to emulsify the grime and along with it the particulate matter.
3) I let the foam dwell and work as I prepare fresh wash and rinse water. and setup the pressure washer.
4) I pressure wash the remaining foam off the car making sure to blast off anything sticking to the paint like bugs and bee pollen (little yellow dots). Before I had a pressure washer I would blast it with a good hose nozzle.
5) I visually inspect the car for greasy road grime that is still stuck on the car. Looks like a very fine filmy residue. If that is present I foam the car again as a presoak and to add a lubrication buffer for the next stage. If you have healthy LSP on the car most everything should come off.
6) Traditional two bucket wash to remove any remaning bug guts and grime.
7) Final rinse and dry.
I usually just foam -> pressure wash -> 2 bucket -> dry since I wash regularly I don't need to do more unless the car is REALLY dirty or not a car I or the owner regularly maintains.
The rinse water bucket after washing is usually pretty much completely clear when I foam compared to a wash without foaming so I feel pretty confident that the foam is doing most of the work without even touching the car.
I find that some soaps are more effective than others in a foam gun but the ones you have tried should all work pretty well for this. I've used DP Xtreme Foam, CG Glossworkz, CG Citrus Clear and OPT Car Wash. They are all pretty good with DP being tops by a small margin but it is $$$.