In the past whenever I've been tweaking derailleurs I've always pulled the actual derailleur wire itself to move the derailleur, like to set limit screws and clearances, so that I'm eliminating the cable tension variable. But I can't do this with my new bike with internal cable routing, because there's only a couple inches of wire accessible in a very awkward spot, and then I can't turn the pedals at the same time because my hand is in the way.

How do people get around this? Or do they just live with it and just do endless back and forth trial and error with cable tension and limit screws etc?

Grab the exposed cable with something like this, maybe: https://www.amazon.com/VISE-GRIP-Ori...00004SBB4?th=1

Shift to high gear. Pull cable tight with your hand and tighten it down on derailleur. Fine tune indexed shifting using barrel adjuster on derailleur. Shift to the low gear and fine tune limit screw. Shift to high gear and fine tune limit screw. No need to grab exposed cable.

You can simply push directly on the derailleur lower knuckle.

But really, set up your stops, then connect the cable and adjust tension. You shouldn't need to monkey with the stops after they are set up, except for tiny changes that can be made under cable tension.

Sometimes people think derailleur adjustments are more complicated than they actually are. The stops are a very basic adjustment and don't require tinkering or readjustment, while tension is just more or less. If the bike isn't shifting right, it is unlikely that it is because of some fine tuning issue.