This is a bit of a joke, how will it escape an R-37M?
Well aside from maneuvering tho, some methods like :
-Jamming
-Towed Decoy
-Chaff etc
can be used otherwise it needs to be able to kill the MiG-31 or Sukhoi platform first, means deploying F-16 escort far forward. This might work with Link 16 transmission, which to cue the F-16, which hopefully can be vectored in advantageous position for AMRAAM employement.
Problem with those however :
1.Russian ground based radars which constrain altitude where the F-16 can be stationed, too low then missile's kinematics become shit as it has to climb up where Russian fighter likely is.
2.Russia's own fighter jets. Well i dont think their anti AEW mission would fly without escorts. These escorts can use their own radars or backed up with A-50 AEW. well hopefully Russians solved their deconfliction issues and not shoot it down. There at least 5 or maybe 6 operational now, 1 is in Syria, 4-5 should be still available for SMO. additional airframe would be beneficial tho.
The Russian fighters may happily launch multiple missiles to help mitigating the countermeasures employed by the AEW. Also they probably wont bother dogfighting after unloading their AAM's.
The other concern would be Russian SAM's like S-300VM do present in the theatre, equipped with 9M82M or DMK missiles if such are available then it can participate in 200-350 km "freebie" shot against the AEW's. Also S-400's might seen 5P61 launchers getting on the theatre soon, carrying 40N6.