I mean, I hear all about how time is 'infinite' but no one seems to focus that Ultimecia wasn't trying to compress ALL time, just various moments of the incarnations of the Sorceress Power.
That's unfounded. There's nothing in the game states that Ultimecia had that much control over TC. The game merely tells us that TC compresses past, present and future, and that one side-effect of this will be that Ultimecia can readily absorb all the sorceress powers throughout time. Further, in Ultimecias scan info in the end, it explicitly states that she is "absorbing all existence", implying she's compressing ALL of time.

You can not compress the infinite for that would just be like well... The natural order of time as the present immediately becomes the past after the 'actual moment' has passed. It would be like travelling to the future 'too fast' and hitting a 'brick wall of oblivion' because the future hadn't been created yet... except in reverse in this case.
Well, the game suggests (indirectly) that the entire FF8 Universal Timeline all exists in full at any given 'time'. In other words the future and the past DO exist, and the concept of a 'present' becomes redundant. However, as you say, if this timeline were infinite it would be impossible for Ultimecia to fully compress all of time, indicating either that the timeline is finite in length, or that she is only compressing the past eras (relative to her own era in time, that is).

Anyway, the "discussion" going on here is on the specifics of TC. Everyone knows what it means in general (all of time compressed to a single point etc.), but not the specific mechanisms behind it. It's those mechanisms, as well as the general nature of time in FF8 which Ryu and Viator are arguing about.

Or, rather, Viator is coming up with outlandish ideas for those mechanisms etc. and Ryu is demonstrating his flaws.