Hey @Too much tech, welcome back!
I understand the need to permanently fix the IKEA Symfonisk Lamps to the bedside tables, but I must say that there is no general perfect position for them.
Mainly it is what sounds best to you, so I would suggest first put them in a way so that you can most take advantage of the empty space on top of the tables for general item placement, followed by a new Trueplay tuning.
If that doesn’t sound quite right to you, adjust them and re-tune with Trueplay until you get it just right.
As you said, the Trueplay is doing the works for each position, it comes to personal preference in the end.
I hope this helps.
When you get ready to mount them to the tables consider a Scotch Command Strip or three as the mounting method. I’ve used these on several items I wanted to stay stable. They even have a strip that has a Velcro closure so you can remove and reattach without using a new strip.
https://www.amazon.com/28-Pairs-Strips-Picture-Hanging-Adhesive/dp/B094QK7WDC/ref=sr_1_3_sspa?th=1
https://www.amazon.com/Command-Heavyweight-Picture-Organization-Adhesive/dp/B09WBRNRHB/ref=sr_1_8
Thanks, may consider the Velcro version.