The remastered version uses the same leaderboard as the PS2 version for Jak 1 specifically, since there is barely any differences between the two versions.

NMS is meant to be the competitive category for all versions. The rest of the versions require the PS2 black label version.

Only Citadel Skip isn't possible on PS3, every other skips you're talking about is possible on PS3. So runs like "no lts" would just mean you have to do Citadel on PS3 which at that point is almost identical to NMS.