Issue with free/busy for single mailbox

I have a very annoying issue with my personal email account, which I cannot seem to tackle on my own.

It seems that I have some issue obtaining availability info and/or MailTips. However, AutoDiscover works perfectly fine, as does the EWS test from ExRCA.Still, on multiple machines in multiple network locations I am unable to see MailTips, check/configure OOO from Outlook, or see availability info in the scheduling assistant. And vice versa, on the same machines, other accounts work just fine.

What's even more interesting, I CAN see the availability info in the calendar of the other person. It even works OK for FEDERATED free/busy. If I look in the scheduling assistant however, I am greeted by the good old 'No free/busy info can be retrieved' message. Another interesting moment is that in OWA, I CAN see the info in the scheduling assistant, again both for same tenant and federated.

If I look from the other side, users cannot see my availability info in either the shared calendar or the scheduling assistant. But again, they CAN see the info for another mailbox in both situations, even for a federated sharing.

I've tried everything I can think of, permissions, profile recreation, Online mode, another machine, another network. ExRCA works fine, OffCat doesn't find any issues, CalCheck doesn't report anything useful either. 

The only thing I have not tried is to move the mailbox to another database, but since this is EO mailbox, I have no way of doing this. I have already opened a ticket with support, but I would appreciate anyone that can contribute other ideas. Perhaps I have missed some test, or you can thing of any setting that might cause such behavior?