Compared to other 20s the MG FF was extremely light and limited to a drum magazine in 1940. However the remove of it's 26kg per wing, not counting ammo, was a significant help. Two MG 17s were lighter than 1 MG FF. The Bf109F's maneuverability enhancements weren't limited to just the removal of armament from the wings, but that was a factor (including the redesign of the wings...but why not the cockpit?). Yes, the 20mm mine shell will kill anything it hits in 1940...the problem is getting it to hit relative to the fire rate and velocity of the regular MG round, which was still quite lethal with multiple hits against a fighter.
A twined MG 81Z is less than half the weight of a MG FF.
Targets of the LW fighters were not exclusively fighters, that includes year of 1940. Cannon can kill bombers and fighters, MGs are less than great in killing the bombers. Two 26 kg MG FFMs are still just as heavy as a single Hispano, while offering twice the rate of fire, and not too heavy for 1000+ HP engine on a monoplane with retractable U/C in 1940. We know that 1st thing people were complaining on the Bf 109F (after the wing & tail problems), was reduction of firepower.
LMG vs. cannon will always offer light weight and RoF, while single LMG it will not match 10% of cannon's destructive power.
With that said - this thread is about ideal fighters (like best possible with then-current tech available) rather than how to improve Bf 109. Thus my proposal for the LW in shape of the V12 powered Fw 190 with the initial small wing, featuring 2 cannons and 4 LMGs, with many advantages vs. a tweaked Bf 109 and far less restrictions.