Is it ever inappropriate (by situation or geography) to ask to be referred to in the tú form instead of usted?
Disclaimer: This answer could be very specific to a region but still answers this part of the question.
Indeed it could be inappropriate in some cases.
I live in Colombia and, even when this is not the case in the whole country, I use "usted" in most cases. It's not always a matter of "formality" and distance, as I use it even with my family and close friends. It's a bit complex to explain because I do use also "tú", specially with women friends in spoken language, or in another contexts like this site, it's more natural for me to use "tú" when I write.
People from other regions use "tú" even in a work environment. For example my boss uses "tú" or "vos" (another informal variant) with me. I always use "usted" to reply to him, and it'd be a bit uncomfortable if he asked me to use "tú".
So I'd say that in most cases it'd be ok to ask someone to use "tú" with you, but there is also possible that some people (like me), depending on their region of origin, could feel a bit uncomfortable to do that.