This is a bit of a tribute to coyot, whose advocacy of the linear play-though has provided many hours of additional enjoyment for me. My single biggest knock against it is the lack of any of the cool reward weapons. To that end, I've played part of a game (up to the first boss battle, which I am maxing power to farm) under the following rules:
Each level (map + difficulty) successfully completed only once. (Get all those stars!)
50% XP and scrap (0% absence penalty, 100% fail penalty).
Gaining the first weapon reward (+14 bow, I think) was really hard, after that it has seemed much easier, but NG+ might get quite hard again, not sure. (Not that far along.) I'm wondering if anyone else wants to try it and see if this is a fun game mode.
It might benefit from a mod that dropped xp/scrap by 60% per level and 20% for starting to try and ease of the starting difficulty while making it ramp back up later - I'm not sure what other ideas make this concept a steady (slowly progressing) challenge, which IMO is the ideal for any linear concept. The ability to bounce between 3 different fronts makes it feel less "stuck" than the normal linear version.
(While a new poster, and late to the game in general, I think I'm fairly good at it already. My first 3-4 runs at coyot's linear mode stalled shortly after healers in NG+, but I finally realized the power of more zerkers, and just hit sheep - which was hopelessly too much HP for me.)
Two other side notes:
Linear hero mode on 300% xp/scrap also seems to be a thing. Try it if you are making a hero mode run.
Chalenges do not appear to respect the 100% fail penalty - I bombed the first one on my first try, and still got 50% despite the setting. So quit if you take damage - but this is technically a bug afaik and might get a fix if it is easy to track down.