I'm definitely not one of those combo people.
How I use training mode now:
Finding the length of normals
practicing execution and input
how to punish/beat moves
block/tech practice
But it feels like I skimp on my training room duties and I'd like to be more scientific in my approach.
Ah, ok, this is a good starting point. I feel like you're on the right track on what makes training mode time effective. I think the biggest thing is to have a sense of direction and not make training mode so aimless. So basically try to have something in mind when you're going in there. For example if you're figuring out punishes, I wouldn't try to overextend and spend hours a day going through the cast. Spending just several minutes against moves in a MU you just fought is plenty enough at times. Aimless training mode can leave you bored and tire yourself out, I really don't recommend it.
Execution, I can't stress enough to not just practice a combo on a stationary opponent. You'll get bored and you might choke when you're fighting a moving opponent. Emulate situations on starting your combos. Do it off of an empty jump low. Record the dummy to move left and right and then try to get a good feel on the range and confirm. Practice off of whiff punishes, practice off of crossunders, etc.
There's no shame in not being able to lab things to the extent of like shadyk stuff. You can let the lab monsters do that for you if you want. Just make sure to have a goal when you hit up training mode. I really suggest using training mode as a way to recall things you just had problems with that day.
Being a scientific player, not everyone has it. And sometimes to be one, you really need a good grasp on the game or how things just happen to work in fighters. I'm able to figure out things like OSes or setups because these things accumulated over time. SFIV is the first game you took seriously to this extent, so don't worry if you're not able to figure out new stuff on your own quickly. It's more important to figure out how to deal with stuff more at the start.