6060 tags in 401 requests, yes, but you can't infer anything about UDTs being read from that. The lack of the debug message does point towards it though.
That being said, there was a bug fix in 7.9.4 related to UDTs and optimization, so if you're not already on 7.9.4 you might see a performance increase by upgrading.
For the most part, yes. Unless you're talking about removing them from the UDT in the controller, in which case making it smaller is always better. There's a practical limit to this, of course: the driver won't read the whole UDT if you're only subscribed to e.g. 1 tag out of 20. If you're not subscribed to all the tags in the UDT it tries to figure out whether it would be better to read the whole thing or just the individual tags.
If they're part of a UDT that has other parts being read faster... yeah, it could be worse, if each group had enough tags in it to make the entire UDT be read.
The first thing to do right now would be upgrade to 7.9.4 if you haven't already. From there, if these controllers support firmware v21 or higher, that would probably help as well.