Could you please elaborate on ways you've found to minimize this "rampup" time?
I find that this is a difficulty with song-form looping and that it often detracts from my enjoyment of the performance. I know other feel differently, but seriously, if you were to notate the song, would it really begin with two minutes of bass and percussion organizing themselves?
One guy who does it really well, in my opinion, is AndrewBird. I heard him in Montreal a while ago and I was quite impressed with how entertaining he is when layering parts.
Notice, in the beginning of the song, how he's performing two parts at once, one is recorded (violin) and one is not (whistling). The performance would not have been as enjoyable had he not done that... Notice how he doesn't bother recording the bridge, but just plays it. Little things that make the performance flow better.
Again very good performance. What works well here I think is the order in which he decides to loop the different parts, the way the layers play off each other. This is entertaining from the first note, there is no downtime... at no point does it feel like we're being taken out of the song by the necessity of looping a section. It all fits nicely together as a whole and evolves from simple to complex. Also notice how he throws in a bridge without recording any further loops (and a coda section by recording part of the bridge second time around and playing it back in reverse, no downtime).
There are more technical tips and tricks, but those depend on your looper of choice. My own music is rarely based around song form these days, so my tricks may not be useful to you, but in any case, I like to try to get a much mileage from what I play. If I record one sound, why not record it into another track with some pitch-shifting or other effects? If I'm playing a melody line, why not grab small chunks of that performance and make it into a bass line? I don't actually play the bass line, but grab bits and parts of the performance to construct it. I don't like that downtime where the audience is asked to wait while the performer creates a background track. My ideal: It's all foreground when I play it and the background emerges from that performance. I'm not saying I achieve this every time out, but it is what I strive for.
Of course, this is easier to do if you're not trying to play back a song exactly like you played it the previous night.