There's hard and soft resets, but your scenario is on the extreme hard end. The core of the issue is that resets delete player agency and the feeling that what they did mattered. This is also distributed unevenly across both players and crew - some people will engage more, and some of the crew members will have got more done, or have more suited skills for the situation, exacerbating certain players getting more spotlight.
The most successful modules turn the reset into a feature rather than an inconvenience, as well as making it a clear part of the puzzle that can be a positive.
In terms of solutions... I think dialing down the hardness is one option. At the moment the reset works like magic, but it could also be an absolutely horrific physical process. If the process is flawed, limited or messed up (or gradually getting worse) then that allows more actions to be retained across realities, and consequences to slip through and persist. The other key source of continuity is puzzle pieces - knowledge is another means of crossing the reset boundary (the main means in fact), so you could make figuring stuff out a more central mechanic.