Keep meshes separate or increase the texture file size?

I am preparing some prop meshes for Unity.
There is a group of them that it seems it’ll be best if I treat it as one unit. Hence I joint all the meshes together. Except now all the UVs are overlapping.
It seems to me that I have to choose either keeping the meshes separate - if I am to keep the same texture resolution for each. Or join them but increase the texture size as to move the UVs around so they won’t overlap.
Am I missing a better alternative here? Or these are indeed my only 2 choices?
If they are, then which one would you recommend?
Thanks guys!

I don’t know whether this would be useful for your model, but look into UDIMs, maybe? I’ve no experience with it in Blender, but I read up on the possibilities a while ago. UDIM stands for U Dimension, where you have an array of UV tiles, each holding its own UV islands and texture. It’s particularly useful if you have a model with different levels of detail. Here’s a decent introduction: