Can you make it its own research that is x10 as expensive as the logistic research?

I can, I would make the multiplier adjustable in that case, since this is a cheat mod (though I don't like cheat mods).
But it would be harder to make the technologies also depend on the previous linked belt tiers (since I want too keep the code generic to deal with any level of ug belts), to do that I would also need to look at the unlock requirements of the technologies, and in the base game Logistics 3 does not directly require Logistics 2, instead it goes via Railway and Production science (not sure, the wiki has contradicting information on this).
So if I do this it would be possible to unlock red linked belts without having yellow linked belts unlocked, which is a bit weird. What do you think of that?

Edit: I think it's at lot easier if I look at which entity(s) upgrade(s) to a certain linked ug, and then make the technology require that as prerequisite. But if due to mod combinations there are two different belt tiers that upgrade to the same tier, I would either have to program it so that both of those linked belt technologies are prerequisites, or so that only one is (probably choose randomly).

I think that all you need to do is use the same research types as the equivalent logistic tier, vanilla balancing is fine even if it doesn't need logistic 2.