Surely this is a lesson in good practice – I'd never jack my T nut up using the bottom of the slot, and my T nuts, both made and bought all have 2-3mm clearance.
I screw the stud in, then I lift up and down to make sure I still have 2-3 movement, then I crack on with the clamping.
If the Nut is tight on the stud so much it can't be held by hand, then stud or the nut's threads are damaged, bent or stretched etc. etc. and go straight in the scrap bin to be reborn another day.
– I would expect the whole clamp assembly to be tightened finger tight, then receive a 1/2 to 1 turn to tighten, so even if it did tighten completely in the T nut, it still wouldn't stick out more than the 2-3mm gap under the T nut.