Whether I perceive front to back cogging or not, what I find far more annoying is sound panned from a main speaker to the center speaker. -----
Just a thought.
Absolutely! And a subject I've harped on here a number of times now.
A partial solution to the "cogging" issue
and what AR describes here is a very simple thing (well kinda simple LOL). Firstly, no matter what anyone says, for best results
identical speakers in all locations is a near absolute requirement. What 2ch audiophile would run different speakers in the L & R positions and then expect excellent imaging results?
Next examine the rooms sound characteristics at each position. Does one corner introduce large amounts of reflection while others are very dead? My open floor plan living room, kitchen, etc; has driven me absolutely nuts attempting to get things equalized to a reasonable extent.

My left side is a wall of windows, while the right side is open to the kitchen for another 10ft. Making the left wall as dead as possible by covering all the window area with 2" thick rockwool sound absorbing material has gone a long way towards balancing the L-R room sound, much more has been and is being done. TBH none of this could be considered to have a good WAF.

Thankfully modern DRC has given us a tool to that can help a lot, but there remains much more to be examined and addressed by the owner.
There is a fortunate few of us who have the budget, etc; to scratch build a listening room and end up with a near perfect listening environment. The rest of us have to live with what we got and need to do a lot of homework, then roll up our sleeves and put a plan into effect to make things as best as we can.
Good Luck