Thank you for suggestions, HellRazor.
I've now installed UO into new folder and ran client via razor from there, connected to shard and no luck.
I've moved the mulfiles folder to D:\ and changed datapath, no luck. I then set the NTFS permissions to allow my user ("alrick") to have full access, as well as SYSTEM user and Administrators group of users. Still no luck.
I'm now setting up my old PC to run client from there and connect to my shard on this PC. If it still fails, there's something in RunUO or the way it handles my PC configuration.
UPDATE: RunUO is unable to write to mul files even when I run client from other PC. That seems to be beyond my comprehension
I was having a camomile tea with my wife and I was struck with an insight!
SOLUTION: make sure that you have map1.mul, statics1.mul, staidx1.mul files in your RunUO DataPath folder, even if your client still uses map0 for moth Felucca and Trammel! I've copied my map0.mul and statics mul files with "1" (i.e. map1.mul) and it worked!