First of all, the woman's not actually doing any weaving in the picture, so she's not really at the "wrong end". It seems to me she's fiddling with the end of the warp (tightening it, sorting the threads?) , while using her beater to ward off the advances of the kneeling man (monk?) who's got his hand up her skirt. In Ecclesiastical Pomp and Aristocratic Circumstance (2000), Nancy Spies further interprets this situation as the woman actually incorporating the man's hair into the warp (p. 100). Secondly, looking at other medieval pictures of weavers and tablet weavers - and at their modern counterparts too - it's obvious that you can sit pretty much anywhere in relation to the band you're weaving; it's not necessary to have the fell (the woven band) right in front of you as long as you can reach it to beat the weft.
As for the rigid heddle, Spies (2000) describes it as a "heddle/warp spreader" (p. 97, my emphasis), which could explain what it's doing in the middle of a possible tablet weaving warp; it's separating the threads and helping the weaver keep the band even. But there may be another, albeit conjectural function for the rigid heddle.
In The Techniques of Tablet Weaving (Collingwood 1996) I found a description of an unusual way to produce a double-faced 3/1 twill. It's described on pages 166-167 and involves both four-holed tablets used standing on their points and a means to raise and lower alternate tablets to achieve the correct structure. Collingwood suggests using a stick and leashes tied around the warp for this. There are no indications that this technique was ever used historically, but when I read about combining tablets and leashes like this, I immediately thought of the weaving lady in Codex Manesse - tablets together with a rigid heddle should work just as well as leashes!
The technique was a little tricky to master. For each weft, the shed was split twice - first by the square tablets standing on their points and then by the heddle raising or lowering every alternate tablet - which meant the final shed ended up being very small. It really helped to tilt the warp vertically on its side to get a better view of the shed. In various medieval manuscripts band weavers can be seen working with the warp in this position and I can verify that it really makes sense to do that if the shed's unclear!
Weaving with tablets and a rigid heddle on the same warp creates many new possibilities! For example, I tried it with two-holed tablets and managed to produce a nice little piece of double weave, combining ordinary interlaced twill with tabby. It might not be a historical technique or the most efficient way to weave complex structures, but for someone like me who loves all the technical stuff behind both tablet weaving and ordinary weaving, it's great fun!
Collingwood, P. 1996. The Techniques of Tablet Weaving. McMinnville: Robin & Russ Handweavers, Inc.
Spies, N. 2000. Ecclesiastical Pomp and Aristocratic Circumstance. A Thousand Years of Brocaded Tabletwoven Bands. Jarrettsville: Arelate Studio.