The car will be concluding a 3000 mile trip so you tell me?, lotsa gloss but surface is not smooth
I'd be inclined to agree with what charlie said. I really do try to avoid all polishing (since it is an abrasive even when used lightly) because it will effect the coating and if you do choose to go with one i'd go with Reflect.
If its not smooth id really recommend Iron X and Iron X Snow Foam...i know you dont want to purchase additional items but they will work well to help restore some of the smoothness. A clay bar or decon towel as charlie also mentioned does risk marring. I'd say give the Iron X combo a try on a panel (rinse car, wash with IX soap, rinse again, spray IX and allow to dwell, was again with IX soap and rinse) and see how much smoothness is restored. I will usually pour a little IX soap directly to the towel im using to wash with to keep it as concentrated as possible in situations like this (its strong so you wont need a ton).
Typically if the surface is not smooth, polishing isn't how i'd approach restoring the smoothness...decontamination is. Since you can't clay, the above is the best decon method I can come up with. If it still isn't to your liking then maybe take a decon towel and after rinsing, while the surface is still wet, do literally just 1-2 swipes over a section, dry it and see if its smooth...and then check for marring. I'd do this only as a last resort though and would try to avoid doing it if possible. Just my method anyway.
Worse case, chances are your top panels are likely the roughest, you could do the decon, then do a decon towel (as you normally would), then do a light pass with a finishing polish, Eraser and then add a fresh coat to just the top panels....just a thought
Let us know how it turns out.