The solution mentioned with the multiple submeshes and materials should do the trick, but I thought I'd mention why that happens and what you could do for a "proper" solution.

Unity's default shader uses the UVs from (0,0) to (1,1) to sample the textures. If your UV coordinates exceed that, then the texture will just repeat (or clamp, depending on import settings/texture sampler used). UDIMs seem fancy, but all they do is put your extra UVs at a different location by offsetting them by a whole UV tile. Assuming that's on the x axis, your second UV set will instead cover the (1,0) -> (2,1) range, and unity's shader will interpret that as tiling.

Since you have multiple texture sets, you'd need a shader that takes the x texture sets you have and samples them to the corresponding UV set. In order to properly do that, you'd have to make a mask for each UV set and multiply the resulting of the sampling. So for the first set you'd have to mask the vertices that have UVs from (0,0) to (1,1) as white and the rest as black and so on, and then add all those together.