So with drop you mean a nose down pitching moment, got it now. In real life being “nose heavy” might create a little more nose down pitch in ground effect but it won’t be much since the aircraft will be in trim anyway crossing the threshold.
In the aircraft I’m currently flying (and operated before) I can’t really tell what the CG position is during flare (nor during take-off as the take-off trim compensates for it), it feels the same to me, the aircraft weight has a larger effect. You do feel the effect of CG very well during de-rotation though.
An aircraft with a forward CG, but otherwise same conditions, theoretically does experience more trim + induced drag so might decelerate faster, and has a higher angle of attack and therefore higher stalling speed. It probably has some effect in real life but not very noticeable.
Don’t know how good FS2020 actually simulates those things but considering your post not very realistically it seems.