Comb-in on instrumental track phase inversion

Just a question. I’ve got a few instrumentals of songs that need acapellas ripped, but there are a few rather strange issues.

Firstly, the instrumental track at times seems to be shorter in length despite covering the entirety of the song; the speed difference is indiscernable to human perception.

Secondly, on attempt to phase-invert, because of the nature of microsecondal speed difference, the inversion would result to a combing-in effect on the resultant mix output. (Flanging effect)

What causes this to happen, if these are essentially the same song, in the recording process? (ie: Is it deliberate? If so, why does it happen only on some songs and not others?) Also, is there any way to perfectly eliminate this problem with some kind of method to sync the instrumental back into matched length? (smooth transition, meaning the speed changes should be smooth/linear.)

Songs:

Nana Mizuki – forgot the title… ??
t.A.T.u – All About Us
Garnet Crow – Flying
Several pop singles.

I was hoping there was like a way for a wave utility to surface, that could evenly omit a single sample *in waveform terms* per number of samples after it, where the sample block size pattern determines the resultant time. (smaller block size, more single samples omitted, and much shorter total time. Maximum possible would end up to be exactly half the original length)

BTW. I’ve tried something like you said in ACID, where I manually determined the exact instance where both the instrumental and original song were simultaneous in song position (as well as waveform position), then used the beatmapper on ACID to sync both to tempo. Results? It helps but it brings up more unpredictabilities in terms of the nature of the waveforms cancelling each other out, and when. (Algorithm issues; they seem to act very arbitrary as opposed to a uniform pattern of omitting samples.) Doing so manually, without beatmapping, is too time consuming. There needs to be a utility that can sorta do that sort of thing (a bit like Sound Forge’s gapper/stutter effect, only you can actually get it to go right on time.)