I realize shortly after writing this that this will probably come off as very aggressive, and for that, I apologize. I'm just extremely frustrated that I can't do anything because my soldiers will just bite the dust if I attempt to do anything, and that nothing will change that.
Have you looked at the different dungeon difficulties? I had none of these issues on the easy or hard mode.
Make sure to include all 4 party members, including at least one of each, and YOU CAN WITHDRAW FROM MANDATORY DUNGEONS at the beginning. Who cares if you lose out on 3 points for ranking up? You can probably get top 3 regardless.
Hard difficulty actually will start you in a lower rank, which from my experience is still more difficult (and takes longer), but if you are finding the dungeons too challenging specifically, you will see more "trivial" and "routine" difficulty dungeons in rank 6 (which is default on hard difficulty).
The true easiest approach would be to withdraw from the majority of tournaments on easy difficulty, de-rank, and then start with the benefits of easy mode without the drawbacks. Independent would be the best way to go to ensure you don't get forced into impossible dungeons by your patron if you are taking this approach. Let me know if you need more help. <3