Dr. George M. Morley has all kinds of fantastic information about delayed cord clamping and his writings are available on several sites.
He advocates delayed cord clamping in twin deliveries.
In our fervent plans for delayed clamping, the OB kept giving stories about how it wouldn't be possible because she'd be busy with Twin B and wouldn't have enough hands to hold Twin A.
Obviously, like so many other bith issues, attendant WILLINGNESS is the biggest obstacle. With the large crew of medical personnel that most hospitals insist on for twin deliveries, it seems ridiculous that there's suddenly a "shortage of free hands" for something as important as this (and that's assuming Mom is too busy labouring with Twin B to hold Twin A herself).
I had writtten to Dr. Morley about the delayed clamping because our twins were mono-chorionic, di-amniotic, so thus at risk of TTTS which can (in rare cases) occur suddenly right at delivery (Acute TTTS versus Chronic - which builds throughout the pregnancy).
Dr. Morley had even discussed a case where he had to deliver twins by c-section, but did delayed cord clamping of both.
Mechanics: If you are "permitted" to birth your twins naturally, a woman's body often has a lull between Twin A and Twin B. (Mine was 17 minutes). So this would certainly allow time to cuddle Twin A on your abdomen as long as the cord was long enough. If it's short, someone else would have to hold babe, just as you mentioned. Once the contractions intensify for Twin B, I imagine it would be too difficult to keep holding Twin A (I had to give my little guy away temporarily). Then Twin B born and resume cuddling.
I think a lot of docs don't like it b/c they want a totally clear view for episiotomy or any of that other monkeying around that they do. But I don't think it makes that much of a difference. Meaning that: even if they clamp off Twin A immediately, you still have a cord hanging out of you when birthing Twin B.
I send you many fervent wishes that your attempts to delay cord-clamping suceed. It is the biggest regret that my husband and I have in the births of all of our children. We always requested delayed clamping. We never got it. We just weren't strong enough / clear-headed enough in those seconds to persist. Good luck to you!