It's NOT about the horsepower, as that only happens well AFTER the car has launched (red light, drag strip tree, or whatever). TORQUE is what moves the car from rest.
I know the Ford 9" has been around a long time and can be built with a multitude of internal guts for the drag racing people. Strange and others can probably build whatever you desire to go into whatever you also desire, BUT they will not be inexpensive in cost either. Not to mention shippini an "oversize" item across the water, if that matters.
What you want, in the type of limited slip differential could well be similar to what GM has been using for years in their pickups. A true locker that has a governor weight that swings out when wheel speed varies a certain amount to lock the axle shafts together. No internal springs, as older-design LSD had.
When they went to this style of locking differential, they stopped using the "PosiTraction" name, but now call it "Locking Differential" in the option list. There could well be some videos on YouTube that were what we were shown in training sessions of how it was better.
One was of competing pickups trying to tow a moderately-size boat up an incline, where one wheel was on a slippery surface and the other wheel wasn't. The Fords and Dodges would only go up about 1/2 way before one wheel would spin and smoke the tire, as the GM pickup continued upward. Another one was where the truck would traverse a concrete gully, with one wheel losing contact with the concrete. The Ford and Dodges needed a tow out of there, but as the GM pickup stopped, the non-contact wheel would spin slowly, then the whole truck would shake, and it'd drive out by itself. A true locker, rather than "limited slip".
The OEM LSDs used springs to keep the clutch plates rubbing against each other, whether 4 smaller springs or one S-shaped spring. The Detroit Lockers were usually in 3/4 and 1-ton pickups, plus some of the higher powered muscle cars of the later '60s and 1970. When wheel speed differential forced the clutch spindle up the ramp, the differential was locked until those forces decreased or were eliminated. A much more severe situation, I suspect.
The spring-loaded "PosiTraction"-style LSDs were "locked until they unlocked", which made for some jumpy tight lh corners in town. The style that I mentioned above, in both the "locker" and normal LSD forms (with the governor weight that determined when to apply the clutches, are "unlocked until they locked".
In the USA, there are SEVERAL rear differential vendors. A good source for shopping information could be
www.SummitRacing.com. They should have all of the main brands listed and you can then do internet searches for those respective brands to see which one might be best.
It might be a good idea to contact the posters in here who have 13-second Chryslers (1/4mile) to see what their rear suspension/driveline upgrades were (other than larger tires) to reliably get to that level of drag strip performance in a 4500lb car! Rear springs. Driveshaft and u-joints, too. You will probably need some urethane isolators to replace the ISO-clamp rubber isolators where the axle mounts to the leaf springs, too. Something which was not used until about 1970 on C-body cars the extra rubber rather than a stiff isolator.
AND . . . when you remove the differential to change it to the LSD or locker style, you'll probably want to also put new side bearings with it, plus pinion bearings and such. Then get it all set-up to specs, for the correct gear engagement pattern between the ring gear and pinion gear.
Now, it's time for you to do your Internet Shopping and investigations. Rear axle and driveshaft in particular.
Enjoy!
CBODY67