Would be amazing to be able to use picker dollies for sub-time movement.
https://mods.factorio.com/mod/PickerDollies

There's an API

You mean "sub-tile", right? ;-)

I do not mind adding support, but I cannot not understand which features of the API are you wanting me to use?
I have no functions in this mod that requires to make use of the updated movement information table.
Or you actually want me to add to the blacklist in movement?
Can you specify?

Sub-tile yes. Not blacklisting no, the opposite.

Ok I assumed that dollies mod fires the on_move event BEFORE it actually moves an entity that would allow to intercept the movement "request" to re-calculate & overwrite target entity coord using sub-tile coord martix.

But apparently, it fires after it moved the entity so you have a choice to either re-position after it moved (kinda hacky) or patch the dollies mod to make it fire events pre-movement which should be trivial.
https://github.com/Nexela/PickerDollies/blob/master/control.lua:Line #157
entity.teleport(pos)

Basically before this line add remote event call "on_move_request" or whatever that would pass event data and return recalculated pos from your mod. This is small change I'm sure mod author would accept.

Currently with your mod there's no precise way to align entities on a sub-tile coords except to pick them up individually and eye-ball new position, I think proposed above is the simplest way to introduce this. You can ofc just copypaste part of dollies mod instead of patching it, but i think it's a worse solution.

I get you now.

Moving the same entity twice will be a bad idea. So I guess it is better for Picker Dollies (PD) code to handle everything about movement.
My functions CSlib.find_nearest_center and CSlib.align_entity() within `lib\CSlib.lua' already has the calculations on current player (or robot) building of such entities. So I guess it requires some work to adapt into PD code.
I do not have the time to do so currently, but feel free if you or Nexela wants to implement this before me.

Honestly, I have not expected users to plan and build with these micro-sized components directly. For example, the constant combinator -3 is so tiny (linearly 1/8 tile, area 1/64 tile) that placing precisely or just connecting wires being plainly impractical (if not impossible).
What I expected is that users will plan and build with the vanilla-sized components instead. Make a blueprint of the whole setup, then compress your creations into scale -3 blueprint with tools of my mod. Then build with the scale -3 blueprint.
By this way, you do not need a microscope to connect wires correctly or place individually. This is why I provided the "Blueprint Scaling" functionality in the first place.