I've not heard this variant before; mind you, I don't know many people from SE USA. Normally the faster pronunciation has a shorter vowel than the slower. (That's not a tautology.)

For example, she's, we've, he'll, they've are "sheez, weev, heel, dhayv" in isolation, but in my connected speech they're "shiz, wiv, hil, dhev". (I don't know how widespread this is among English dialects.)

As to alternants, do you have one with to too? I use schwa [@] before consonants and slower [tu] or faster [t@w] before vowels.