For purely educational purposes (wink wink) what is the theoretical maximum number of characters I can have in a custom string property on a perspective component?
I've seen the limit for memory tags, does that same limit apply to custom properties on perspective components?
I imagine it would be that limit minus all the characters taken for the actual view configuration.
Java strings can be ~4GB. Somewhat less than that, I would presume.
you're putting string encoded view json into custom properties in your UDTs, aren't you? 
Long before you hit Java or JS string size limits, you'll bump into limitations syncing property messages:
Marking properties as private will help with this (as we will no longer unnecessarily sync custom properties to the frontend), but I'd still expect you to start getting issues with things like saving your project in a timely manner and general slowdown/weirdness as you give us a way bigger value than we're "expecting" way before you hit the max length of a string.
I wouldn't put more than a few thousand characters into a Perspective property, and even then I'd question my design assumptions and be actively planning a different solution.