I should of course myself have discovered this earlier on, but after connecting the tonearm from the 153 to the 156A, and also already having serviced the motor, I just tested that the motor was spinning well after being winded up, without playing a test record, before I quickly moved on to another project.
Unfortunately I do not have the old tonearm for the 156A around me this weekend, since it is stored in my repair room, that are 30 kms away. Are you (phonosandradios), able to check the difference in length between the two tonearms? If you don't have a Columbia portable with a plano reflex arm, I will take some measures, and also upload a photo, so we can check if they are of the same length. Maybe it is as simple as using a tonearm from a Columbia portable? I am just thinking loud now, but some measurements should be able to tell if we are on the right path.
The question also arises of course, in how many different sizes were the Plano Reflex tonearm made? Let us hope it is only two, if so, the problem could be easily solved. I also admit that I was too lazy to remove a plano reflex arm from a portable before buying the scrappy 153, being too caught up in our conversation here, and not being as practical as I should have been. Maybe I already had the correct Plano Reflex arm available in my storage room on a donor Columbia machine

I upload two photos, the tonearm from the model 153, and the tonearm on a portable 202. They are measured exactly the same way, with a 90 degree at the end of the tonearm, visible on the photo taken inside the 156a ( but impossible to see on the 202 photo, since I am alone and can't have a third hand to hold the camera.

The tonearm base are different on a portable and a floor model, but without knowing the Plano Reflex arms too well, I hope all the parts around the base on the portable are removable, and can be exchanged to the parts found on the 156A. This far, I have only cleaned and oiled a Plano Reflex. I know they have pretty small ball bearings, and possibly also other issues that must be considered. I know there are members on the forum who are well experienced with servicing Plano Reflex arms, myself I am not there yet, but for sure I will dive into this trying to solve this problem with the 156A