The largest tires that fit in a 69 Barracuda are 325/50-15s on 10inch rims.
Second largest are 295/50-15s also on 10s.
The standard backspace on those is 4.5 inches.
To install those. you will have to move the spring inboard to at least flush with the inner wheelwells.
Then you will need to narrow your rearend to move the wheels to that inner well surface less 3/8 inch per side, to allow for body sway in the turns.
Then you will still need to roll up the outter knife-edges vertical to prevent the tires being cut.
To prevent you having to narrow the rearend, you can increase the backspace to about 6 inches, but for 295s you will still have to move the springs.
My conclusion is twofold;
1) you are not trying to fit the largest tires that will fit, and
2) you got the wrong backspace wheels.