You could fit a small IR seeker on her - presumably, some derivative of Stinger's one - much easier than on AMRAAM.
Back in the 1960s and 1970s at China Lake NOTS experimented with something called the Sparrowinder (It's mentioned in Ron Westrum's book on the Sidewinder) where basically the seeker from an AIM-9D was mounted in the body of an AIM-7E.
They may even go as simple as adding a small, narrow-angle IR sensor to radar fairing
It was called the AIM-7R.