I upgraded my '69 Sprite to 3-point non-retractable belts, and then later 3 point retractable belts. Like you, I just feel uncomfortable in a car without seat belts. My daughter kept slipping out from the non-retractable belt, so that's why I went to retractable units.
I plan on recycling the 2-point and 3-point non-retractable belts that I replaced on the Sprite for use in my '53 Plymouth project, which is completely devoid of any seat belts.
Retractables don't do you any good unless they lock with accelerometers as in a collision, they will extend out and you slip out, Been my experience anyway.
On using your old ones on the 53 Plymouth.....better czech length and waist size first.
When I put lap belts in my 50 Ford Tudor, lord, 45 years ago, got some out of a 67 Galaxie, retractable, non-adjustable, and the seat is taller, bigger, barely connected. Then 45 years of waist expansion, I'm there. They still work, but just.
My guess is, OTTOMH, the seats being much lower and smaller in the LBC, you may not have enough belt to extend out. Better to czech first than drill and fit and find out you can't even belt in a rolled up newspaper.
My Jag has front three-points, lap and single shoulder...to adjust, get out of the car, on yer knees in the pouring rain, and work the belt through the adjustment buckle near the floor mount.
I have driver's side set, passenger we just move the seat back and forth to set.