Reporting back on my experience.

On 15 October I initiated a 7,113 Marriott points transfer to Qatar to top up for an award. Nothing by the 6 week mark (26 November), so I opened a ticket with Marriott. On 14 December, I finally told Marriott that asking for my patience while they look into the transfer has been going nowhere and insisted on exploring other options.

I suggested that Marriott gave me some points so that I can attempt the transfer again. They offered 6,500 points, which they said was on a one-time goodwill basis and the maximum they can offer. At this point I didn't want to argue anymore, and I had some leftover Marriott points anyway. So I made a 7,117 point transfer (which gives 1 additional mile over at Qatar so that I can tell which transfer had made it).

I checked my Qatar account today and both transfers have gone through, thus ending the saga. Wiki updated.

Looking at the wiki, it seems that the problematic transfers were initiated back in October and that Marriott has sorted out its IT for now. Also, it could have been coincidence, but sending the second transfer seemed to have "unclogged" the pipe and sent the first transfer through.