Most of my work is restoration of old sash (like Jade) and I make the needed millwork as required when I can. On a private residence you can do what you please, but on many projects I need to stick with orginal methods and materials as closely as possible.
Couple of things to point out. In the pictures of the door, I see water staining/discoloration and no bedding compound for the glass. If you don't protect against water intrusion, no method of repair will last. There should be some type of bedding or caulk used aournd the perimeter of the glass once the final repair is made. Also, as for making the trim, I usually do not sand much at all. I use shapers and moulders (yes - this is equipment several steps above what average homeowner uses) to make clean cuts with a minimum of fuss. As for shorted segments being outside - I always seal end grain before assembly so that really is not an issue.
The photos below show a sample of some moldings made for an arch top window and then the process of making the arch top itself for a replacement sash. Note the picture with the tennon trimmed and pegged and see how the grain slope is minimized. In this case I used three segments instead of the original two and used better joinery for a much stronger window. Final installation photo is at the end.
Three segments laid out over MDF guide base. The segments are cut and then fastened to the MDF base, which is then flipped and used with a flush cutting bit with top bearing in the shaper table (with a router adapter in this case).
After trimming, the piece has been flipped back over. The trim bit is visible.
A floating tenon is installed.
Tenon has been pegged and trimmed. Note relatively low slope.
Finished arch sgment. The MDF base was still attched as this went though the molder, maintaining the curve without any interaction on my part (sorry no pictures). A rabbeting cutter was used in the shaper to make the glazing rabbet. Next step will be final assembly and glazing.
Finished window installed in a clocktower.
Big Barn, Little Barn, Saltbox, Cape, 2 storey Farmhouse - and a shed to boot! 237' end to end. This could take a while.....