2004 idles rough at startup and loses power briefly
 

I have been trying to solve this problem for about 1 year and a half, and after a four trips to the mechanic am at a loss of where to go. my 4.7 v8 runs great - mostly. It starts up fine and then as it starts to idle down to normal, it starts to shake and runs rough as it drops under 1k. If i do nothing it'll shake for about 10-15 seconds and then continue idling down to about 6-700RPM where it settles in and then runs perfectly. If I attempt to drive it before it's down to a normal idle it'll lose power - I can put my foot on the floor and the engine will sputter like it's going to stall and then after 10-15 seconds it'll take off like a bat out of hell if I still have my foot down. Sometimes I can smell a little fuel briefly when my foot is down and it loses power. Runs perfect after that - I can drive all day with no issue. But - if I turn the engine off for 5-10min - it'll do the exact same thing again - every time I start it. Doesn't matter if it's a hot or cold start, and it's really only a problem immediately after starting - no issues any other time. I've replaced the TPS, IAC, cleaned the throttle body and poured tons of dry gas and fuel injector cleaner into my tank. I've also had recent cats all O2 sensors replaced. I have a MAF sensor that I have't put in yet, but I'm not really hopeful that's the problem. No idea what to do next and my mechanic can't seem to figure it out. Any ideas?

Sounds more like a programming issue to me, than anything else, especially since it is easily repeatable.

how would I resolve that?

Talk to the dealer, see if there is a software update available.