Originally Posted by gerundium

Coming back through the caravan after a flat is in part a learned skill but you have to realize that the pro's make it look way easy. It is usually said with us that you need to be above average strong to get back on, of course it is slightly situational.

only advice i can give you on that front is the following:

- drafting:
you have to be seriously right on the bumper. any team car in a serious race will have a scratched up bumper from the occasional front wheel taps. when you are with multiple people counter-intuitively you want to be the front guy, the guy on the car bumper gets a way better draft than the guy drafting the rider behind the car. (obvious solutions is to ride side by side on the bumper)
There are regulations on follow cars but i don't know if they apply in the US. depending on the car and your bike position either look through the rear window to see where you are going or look over the roof of the car. use hand signals to communicate with the driver / mechanic to go faster slower.
when the car is taking you back up to the rear of the caravan you should be able to go about 10 km/h faster than the pack. i've been a mechanic in a car going 60+ km/h to get someone back on on flat roads. don't overdo it though as you should still have some punch to make the last jump to get back on when you leave the draft of the car.
when you are back in the caravan don't be a hero and try to get back on too quick. just sit in the draft of the cars and when they bunch up before corners they should leave the inside open, that's your chance to move up two cars for free. the last bit at the front of the caravan is always the hardest, as they will hold a gap to the rear of the peloton. this can be closed in the same way before a corner usually.

of course if you are really strong these tips apply less and you can overtake cars on straight roads etc.

if there is just one neutral service car it's going to be harder to come back, as they will drag you up to almost the group and then usually they stick you out in no-mans land as you mentioned. Then it's all about being strong for the last bit.