AMP deaminase deficiency is a new one for me, but according to
Wikipedia, AMP deaminase is an enzyme that converts AMP to inosine monophosphate (IMP). Since conversion of AMP to IMP forms part of the pathway by which AMP is flushed from the body, leading to PEM according to the theory (see
this post), my first thought is that if you had the usual virally-triggered ME, you might actually be less prone to getting PEM.
Looking at the Wikipedia article, AMP deaminase deficiency seems quite complicated and not very well understood, so it is hard to suggest anything. The article does say that one of the issues is loss of ribose and fumarate, so you might want to try taking D-ribose and fumarate, if you are not already. Also it says that low levels of nitric oxide may be an issue, so some NO boosting supplements like arginine and dietary nitrates (eg beetroot juice) might help.