It wasn`t really a reprogramming..it was a fairly significant hardware change,RWR of the time was more directed toward pulse threats not CW..to pick up CW you have to redesign the system..It would have been a lot more effective if the US hadn`t sent a large number of replacement F4`s with new weapons and systems and then had the instructors from Nellis flying them in combat for the IAF.
As for missile warning it depends on the system pure SARH is a bit of a rarity in the west these days,the AMRAAM having a datalink rather than relying on beam riding i suspect would make lock and launch detection a bit more problematic as the launching platform doesn`t have to constantly illuminate.
This probably explains the increase in Missile Approach Warning systems and UV flare detectors in more modern platforms.