Nah, they tried that with the F-4... and they ended up having to retrofit a cannon to it for close-range dogfights. Missiles just allow you a chance to begin the game early, and hope the other pilot can't counter / evade the missile. At those speeds, the distance closes quick... and when you want to maneuver, you have to slow down. Actually, maneuvering itself slows you down. The optimal speed for dogfighting still is ~180 m/sec, because then you can turn faster. BTW, what's the max speed of an F-14/15/16/18
without afterburners? Ask yourself this: If your afterburner uses so much fuel that you run out in 20 minutes, how often will you use it? What will you use it for? You won't use it that often, except in short bursts, for added speed / assisting during maneuvers. The F-22 is unique in that it has
supercruise, which means that it can travel faster than the speed of sound (Mach 1.5) without using its afterburners, thus saving fuel. (Max speed they will now confess to is IIRC Mach 2.4... give me a break

)
So, the solution to your problem is to make the afterburners have enough fuel to run for about
10-20 minutes to make it playable, put 2-5 minutes, with 0 recharge rate, a
max norm speed of
570 mile/hour (mph) = 254.812 8 meter/second
and an AB speed of
2.5 mach = 850.725 meter/second
... of course, the AI doesn't know how to handle that... but for multi, that would work.