You could modify the existing sash, and do what you describe. I don't know that the benefit of doing same will be realized in any great amount, you are in a more moderate or temperate environment, so the thermal transfer from a single pane to an insulated pane may not be prolific. Its certainly better than single pane glazing, and likely to not be all that difficult to do.
You would have to design the modification and check that everything works, so maybe you make a few sketches, detail it and see if anything is a problem.
If you can modify the wood sash to fit insulated glass, (speak with the local glazing or glass supplier) then detail the glazing pocket out for the new glazing. The glass supplier can provide you with the size you need. The area in the sash that is open and or clear is referred to as the day light opening or DLO, and that overall actual dimension should deduct for necessary room for the glazing,(expansion) a glazing gasket, glazing setting blocks if used or necessary. You don't want a precise and or exact/tight fit for the glazing, it needs a little room and your glazing supplier can help you once the dimensions of the modified sash are known. I'd want thin setting blocks on the bottom, a glazing gasket or something between the edge of glass and wood sash. Its possible you could pin the glazing with points or install a glazing trim/retaining piece or both like you mentioned, you do want to make sure the glazing is secure.
New windows would likely perform better seeing that the units by themselves will likely have better performance specifications, stand alone, but the installation is where it counts, so the rough opening and surrounding areas are insulated, and as a unit within the wall, as an assembly is where you get better performance. The best made window won't perform unless its installed properly.
I re- glazed a sizeable bow window that got hammeered from the elements about 15 years ago. The contractor doing some work here, said he could not do anything with it, has to be replaced, not only did I dis agree, I proved him totally wrong and literally rebuilt the window where the wood, (mainly the sill and the 2 operating sashe bottom rails) was deteriorated. Once that was done, I measured up and ordered all new glass, installed it using push points and glazing compound, primed and painted, its just now needing paint again, and though it does sit under a decent overhang, the weather from the west does get to it if its a strong thunderstorm or similar, so its well protected but gets the weather at times, there is one on the opposite side of the house, under the overhang and the unit is like new, but is of the '78 vintage.
In the bitter cold, I cannot feel much if any thermal loss or transfer, it was a lot of work mind you, but a rewarding project when I can see 40 miles out that window clearly and that following winter when the draft from it was eliminated.