Hi,
The negative stage must be aligned with the easel. Assuming your easel is completely level (which it should be, if it is not a battered speed easel or a bladed easel with missing feet), you can use the baseboard as well.
I don't know enough about that particular enlarger to tell you where the alignment hardware is...but I am almost certain that it must be there. Even my cheesy Omega B22 was align-able two ways (and believe me, I had to align it OFTEN), and the Beseler is a better enlarger in many ways.
I am 99.9 percent certain it is not your lens.
The big thing that will throw Beseler enlargers severely out of alignment is if the left and right gears end up at different points on the left and right columns; a "jumped" tooth on one of the two column racks. Omegas, Dursts, DeVeres, etc. do not have this problem, as they use only one column. However, you already have achieved alignment in this axis, so I think you are OK. It would also be very easy to see this with the naked eye if it was happening.
As I said, I do not know the 23 models well, but the 45 models have a lens stage tilt, which is actually a great feature to have. I have used this feature quite a bit when shooting with cameras that have no movement or limited movement (such as my Speed Graphic, which has tilt, but no swing). It is possible that if the 23 has this feature, the lens stage is not level to the film stage. Again, this would be along the axis you have already successfully aligned, but you definitely want to look at it.
What you need is the instruction and/or service manual, which I am sure you can get either second hand or from Beseler proper.
Good luck. It is a pain, but entirely worth the effort, so stick with it until you get it right.