Short story: I convinced Orion to stay, and returned to Kreger. He tells me to talk to Daisy. I talk to Daisy, she gives me power armor and training. ~5 seconds later, the game crashes. Didn't have any other issues so far with the quest.

I don't think this is systematic, as I had no issues getting the Power Armor when I did this.

If you exit the game, restart the system, and then try to get the armor again, does it crash?

Yep.

Thing is, it has to be ~5 seconds of unpaused game. Activating Pip Boy for once prevents the crash until I close it again.

Console commands welcome, and info on what should happen after I get the training. Is Arcade going to return?
EDIT: Disabling the few mods I have didn't help.

Add the power armor training perk via the console and see if it still causes a crash.

I got it working with some modding.

In the GECK I made two activators: one that upon activation adds PA training and one that adds Remnant armor and proceeds the quest to its final stage. In doing so I also removed time skip in the training (8 hours) and condition check for PA training.

I placed the activators in vertibird hangar, activated the PA training activator first and then the armor/quest one. I successfully got the next objective, to leave the Remnants in peace. To do this I entered their conference room and exited back into the V-bird hangar. Quest completion triggers and everyone is happy.

What mods can't do..

I had this same crash. The problem was that the time variables had been modified (Imp's TimeScale Adjuster - v1.4 fixed this error).

Setting time scale back to the static timescale of 30, the default, fixed the problem.

This also happens in a couple of other places. For example in the endgame where you speak to the Ranger at Nellis about the President's visit, any modified timescale may cause an immediate crash.

The rule seems to be where any forced passage of time inside a conversation may occur a modified timescale may cause a crash. The exception is sleeping or waiting which does not crash.

I see. Figures, my timescale is set to 5 since I really don't like the way days last only 15 minutes or something.