In 1948 the F-86a set a 670mph speed record, in 1952 a F-86d set a 698mph record, in 53 F-86d set a 715mph record.
In 1954 a J29 set a 500K record of 601 mph and in 55 set the 1000k record of 559mph. And it's listed top speed is 660mph.
The F-86 had some ultimate speed records, the J29 had some speed records over distance, that the F-86 might or might not have been able to exceed.
I'm not too sure how a fighter with just a 6000fpm max climb would be able to cope with a fighter with a almost 11000fpm roc ability. ( Mig 15 )
Granted, the J29 may have a 2000 ft higher service ceiling, and 20mm cannons, but in every other performance category it falls short of the F-86, especially in roc.
Getting back to the original question, check out the rear propeller clearance when the aircraft is nose high, you'll see it's a impossible dream aircraft.