I'm just curious on how timing works in Gamma stages. Is it 3 minutes minus the time at finish, or is it the time it takes to finish in elapsed time?

On the standard leaderboards, the runs are timed by taking the start time (3 minutes) minus the finishing time, plus the time bonuses you get during the run. This gets you the time as if the stages had a regular level timer like any other character.

For example, my Hot Shelter run. Starts at 3 minutes, ends at 2:12.26, and gets 5 bonus seconds from lockons during the run. 3:00.00 - 2:12.26 + 0:05.00 = 0:52.74

If you don't wanna have to calculate it yourself before knowing what time you got, you can download "External IL timer" from https://www.speedrun.com/sadx/resources, that does it automatically for you.

On the Category extensions page, we have a highscore based Gamma level leaderboards, so there you can play the stages with the intended goal, of racking up as much time bonuses as you can and what's shown at the result screen is what counts. Those are not the main leaderboards though cause that's not really beating the stage quick https://www.speedrun.com/sadx_extensions

That makes sense.