The blind nuts will have a shoulder on the outside such that the plate will stand off from the mast - this may be tolerable but will allow water
behind the plate where you can't see it. I never like that.
Countersunk blind nuts are an option but you would need a thick enough mast section to use them. There may be some specialty ones with very wide flares. However thisis all complex.
A common fix is as HyLyte says although rather than bolting the plate to the mast I would rivet it. Fabricate a plate that is blind riveted on and the gooseneck plate attaches to that.
The advantage is you can use a suitable number of blind rivets, properly bed
the plate and have a repair that lasts a log time.