Like you I have never had much luck using the 4-5-1V against 4-4-2.
I have switched to either narrow diamond (i know it's not what you want to hear) and had success with that or against weaker opponents just face them with the same formation and overpower. For the diamond, i used it when the opponent was weaker in the middle (for example weaker DC/MC than DL/DR/ML/MR.
4-4-2 vs. 4-4-2 against a weaker team I've had good success with down the flanks attacks, attacking (hard attacking if the need is there), whole pitch pressing , zonal marking, no counter/offside trap and normal tackling.
So honestly, not much different from what you already have in your head
Edit: the best result i ever had (4-1 against a slightly stronger 4-4-2) was with a slight variation on the 4-4-2. using an "S/Z" formation, simply because the players I had available demanded it. It worked well. AMR instead of MR and DML instead of DL. That was a mixed passing.