I purchased a BT HomeHub v1.5 for a tenner from ebay. It's running the same firmware as the v1 (6.2.6.E) that is my broadband router / DHCP server / primary access point and as expected the problem is now solved; when connected to it the MX200i has had not a single loss of connectivity from any internet radio station or when streaming from the media server. My trusty DG834G v1 is now back in the drawer waiting for another occasion that requires it be dusted off.
For the record, Ancient Observer to respond to your comment elsewhere; despite the intensely pink product it's connected to, the antenna remains outside the MX200i case per my modification because testing with the V1.5 HomeHub showed it's worth another 15% wireless reception strength. It's modesty is protected however because it's now entombed inside a child's thin plastic sweetcorn cob that (a) protects it and (b) seemed kinda appropriate for it living in a shed!