Ok, but why not do nothing and just play the mono LP in stereo and bob's your uncle?
Unfortunately for you Todd, in this case your uncle is not Bob but Tom!
To explain why I will have to put on my old UND associate professors hat.
The basis of the problem lies in the fact that speed is a scalar number but velocity is a vector. So speed has no phase, but velocity does.
Let me try and explain the significance of that.
Let us take an imaginary old disused aerodrome with two mile and a half runways intersecting at 45 degrees at the midpoint. One going East/West and the other north east/south west
Now take you car at the aerodrome and travel a mile east at 90 mph. Now turn round and go back at the other direction west at 90 mph. Making the time for the journeys the same. Now cross the midpoint and continue west at 90 mph for another mile.
Now, your speed will be 90 mph for the whole trip. At the easternmost point your speed and velocity are 90 mph, but your velocity average for the trip as you pass the midpoint heading west will be 0 mph, and your velocity at the mile west point is -180 mph.
Now lets have you travel northwest a mile at 90 mph. Now if you draw a line down from the half mile point to the line going west it will intersect at the midpoint. You speed is still 90 mph, but you velocity relative the the midpoint of the west heading is 45mph.
So the point is that speed is a scalar number, but velocity is a vector having both magnitude AND direction.
So when you go back crossing the midpoint there is an antiphase condition.
This does apply to playing your mono record.
Now, a mono record is just a laterally modulated groove. In other word the stylus is going up and down that east.west runway.
No let us put another runway at crossing the midpoint going Northeast/Southwest. That is the exact condition of a stereo groove cut. The coils are position in just the way to detect northwest/southeast stylus movement and northeast/southwest movement of the stylus in this example.
That is how you get the left and right channels. It is only possible because velocity is a vector and the cartridge reacts to the velocity of the stylus and NOT the speed.
So I think it is now possible to see why playing a mono record in stereo is way suboptimal and why your uncle is not Bob.
If you couple the channels and make it mono then any extraneous up and down movement of the stylus, in other words deflections that are not strictly lateral will be cancelled totally by being antiphase.
So when playing mono records always engage the mono button and couple the channels. It is also best the play from single speaker, like I demonstrated to you if possible. That really depends on the competence of the center channel and a lot of those are "week brethren" to say the least. So coupling the two channels and playing from one or two speakers could be the best option.