Being a lameduke / beta duke nut myself, I'd go with on fixing the lameduke maps.
Lot's of the maps in there have very neat concepts and even an complete gameplay flow.
It will be a pain to fix them since some of the effects abuse the build engine (and break up often).
Also most of the maps lack in detail and have pretty bad design.
Best bet would be to cut an episode, combine some of the smaller map designs in existing maps or drop some.
I would place it as the closest I could get as a duke3d sequel/prequel since you can clearly see some of the original/old 'duke style' in most of the maps.
Not sure who did what maps but It's still the same people who worked on the game. So many levels/ideas got scrapped that you won't really be remaking the retail duke3d levels.
Making new maps is also good, but it kinda breaks the above point. I see it as slapping existing custom maps in a mod.
Modifying existing maps.. well that would be cool as well. Since both are 'official' (lameduke assets/gameplay with retail maps).
It would need hand modifying to make them look good though. These could be distributed as patch files so the original map data won't be distributed.
I really liked the Red light district texture swap screenshot so I think that a complete swap would really change the mood & give the illusion of an earlier version
I would go with fixing the lameduke maps.. but!
In the end it's your choice, I am just excited about anything that is lameduke related stuff.
Just giving out my opinions