Hi,
I've made an early 14th century garment in the style of the 10 panel dress (Norlund N. 45 /D10587) and found that a fine wool twill, unlined, will drape beautifully around the body, giving lots of shape without being tight. That should work for your garment in the Codex Manesse style

The Ronbjerg Garment (D2625a-e) in Woven into the Earth, which is radiocarbon dated to the late 13th century and therefore closest to your chosen period, and quite a few of the other women's garments in the book have a rather narrow middle and wide side panels. I found that gives a much better shape, and leads naturally to a curved armhole and sleevehead (the armhole curve is in the top of the side panel, so the armhole goes straight down along the middle panel, and then curves downward along the side panel(s)).
I started with rectangles for the major pieces (front, back, sides) and triangular gores to widen the hem (front and back, sides if you want to have even more width at the hem) . The gores I use are cut from rectangles, cut in half diagonally (remember to leave some space for seam allowances, so move the diagonal slightly inwards, top and bottom). Two pieces form one gore. Wherever possible, sew an edge on the bias to an edge on the straight.
I tacked all the pieces together, and tried it on. Then I just pinched in the seams where I wanted a slightly better fit. When I took it all apart, it did look like the drawing of the 10-panel garment

I only cut off less than an inch maximum on each seam, so there wasn't a lot of waste of material.
Sleeves should be tight on the lower arm, but make sure you have enough room around the elbow. If the Moselund garment is anything to go by, you're ok for your period to fit a slightly curved armhole, which gives a much better fit on the upper body, and more movement. If you keep everything rectangular and add underarm gussets, the top part of the garment (body and arm) never seems to have that smooth quality of fit and movement that the paintings portray. You can either sew them shut every time you wear the dress, use buttons, or for a more lower-class fit, make them just wide enough to slip on.
Unfortunately, I haven't got pictures of the dress yet.