I had the same idea of heating the tabs. I did not remove the old worn nut myself, the retired guy did it for me. He also put the new one in. I am not sure there was a notch for alingment inside the tube, the only notch is at the end of the tube in the photos, but even if there was he probably obliterated it expanding the tabs with his tapered mandrel ( all speculation) . If it weren't for covid I would do the work with him and properly :/Let me see how the nut aligns in the tube to be captured by the tabs.
Looks like you cut one to get the nut out, right? All of my actuators are Saginaw and Houston Trackers because that's what was sold here back in the day and so far just pumping grease into them and wiping out the old gook that squishes out has worked well.
Can you weld the tabs back and then squeeze them back to capture the nut after it's all cooled down?
Is it possible to lay out and drill, tap the tube tabs or perimeter for something like 4 set screws?
Perhaps drill the nut body so the screws go into it far enough to capture but not interfere with the acme screw?
Tap carefully for a real good interference fit and so they go in flush with the tube?
Finish it off with red Locktite so everything stays put?
Hah. I'm cussing you TV, I was out in my shop before my first cup this morning and got greasy as hell running my tubes out to see if they looked like yours.
I'm compelled to add it looks like you used copper anti seize for lube. I'm not sure how it's going to gook-up in time and is why I'm sure a good black molybdenum or synthetic grease wouldn't be better. Plus if you drill your outer tube for a zerk in the right place you could pump more in periodically.