67-69 barracuda front tire width

The better question IMO is what is the biggest size tire that you can put on a 7" rim. And my answer to that would be a 205 for cornering and a 215 for not.From a streeter's perspective (me);
On the front;
If you put a 215 on there then you will have to drop your tire pressure for optimum treadlife. And then it won't corner worth a fiddle-fart. At about 26psi, the tire will begin to roll over and pick up the inside edge off the road, while getting dangerously close to running on the sidewall. By 24 psi it feels like crap in the corner. For cornering, IMO it is better to run more psi, to stabilize the tread. The 205 will run probably around 29 for optimum treadlife, and you can bump that to maybe 32, or more, for spirited driving.If you plow around a turn with the fronts at 24psi, and mount a curb , you will be buying at least one new rim.
If you hit it at 32psi, there's a good chance you'll bounce up and over it; that's if you have the presence of mind to steer into it at the last moment. I have saved my aluminum slot-mags that way many many times.

On the back,
same thing except now you have the tires trying to simultaneously deal with the power application.

Yes I have a 68 Barracuda.
Up front,I run Sbp 235/60-14s on 7.75s at 29 for treadlife.
On the rear are BBP 295/50-15s on 10s running 24psi for treadlife.
With anything 275 or less out back, that pos stinking car kept spinning me out, pushing me up on the inside median and facing backwards.Talk about oversteer. Okay, I admit it, I stayed on the power too long hoping to ride it out,lol. Anyway 295s solved that. Now I can slide around any turn with no regard for the amount of rubber that is peeling off my tires. Ok wait; they're BFG radial T/As they don't peel, they scream and beg for mercy, but I digress.
To answer your question;
The biggest tires I have fit on my 68Barracuda were; 245/50-15s on barely big enough 8s up front, and 325/50-15s on not nearly big enough 10s out back. As a streeter, it wasn't all that much quicker/better/whatever, than with the 235/295 combo; but with the sticky 245s up front, I could get away with doing stoopid stuff more often. 235s take some finessing. and horsepower steer. and run-off room when she goes into 4-wheel slide mode, cuz it doesn't always go where you think it will, when that happens..
EDIT
Oh also, when yur sliding sideways, the brakes make it worse,usually.