How to split large UV/texture into 2k tiles

Hi guys,
How would approach following task:
I have an object with a single material and a single large texture (22k). I need to split this texture into a set of 2k tiles (preferably with a similar texel density) to get as a result the same single object with multiple materials assigned and each material using a separate 2k texture (separate image file).

I would greatly appreciate any hints as I’m struggling with this conversion since a couple of days.
Cheers!

You can create multiple UV maps.

Technically, you would approach this by using UDIMs. You would need to create a second UV map for your object and spread out the various UV islands across different UV tiles (0-1, 1-2 and so on). Then, you would bake the original texture data (using original UV map) onto a new tiled texture using this new UV map.
However, while Blender does support UDIMs for texture sampling, its built-in baking, as of today, doesn’t yet bake to UDIM tiles (among other things) - it will always bake only to the first 0-1 tile. So if you want to do everything in Blender, you’d either need to find an add-on that helps with baking UDIMs (I think I saw one at some point), or do it the tedious way by baking one tile at a time, repositioning UVs, baking again, etc., and then combining all the images into a single UDIM tiled texture.

Yeah, UDIMs would be very handy in this case. I already found that UVPackmaster is able to repack a single UV onto a given number of tiles, so that part would be very easy. I didn’t find any addon that could bake from the original object to a UDIM though.
I’d like to avoid manual baking. I got quite a few objects to process this way…

Are there any free or affordable apps that could do the job easier than Blender?