Ha. by "lots of RST action" I meant that many of the calls to the MS servers were being responded to by RST packets by their systems. Because the range and quantity (sometimes just a few, about 10 in a row; sometimes a lot, upwards of fifty, followed by a pause of 5-10 seconds and then another round, etc…), and the fact that they were happening on IPv4 as well, I was tending to rule them out as a factor at all but included the mention for completeness...
Since originally posting, I've had to travel a bit and some locations were offering IPv6. However, they all worked! It turns out that in every case, despite having a v6 address, DNS resolution always pointed to IPv4. So much for that!
Because of that, I also agree that by resolving their servers in IPv4 will be the fix du jour - until they get their issues resolved.
Having worked with MS in the past, the best way is to do as much research as you can prior to contacting them. Which I'll do again shortly (and report back if something useful comes of it). This discussion has been a great help for that.