Thanks for the feedback! I agree with a lot of it, but there are a few things about the loyalty system that I don't do a very good job of explaining anywhere. The main thing is that it requires exponentially more XP for loyalty to improve at higher loyalty, making it difficult to achieve high loyalty levels, but very easy to recover from low loyalty levels. (At least, that's the goal.)
Loyalty Level | XP Required to Improve |
Mutinous | 800 |
Openly Insubordinate | 4000 |
Insubordinate | 20000 |
Doubtful | 100000 |
Indifferent | 500000 |
Confident | 1500000 |
Loyal | 4500000 |
I tried to balance this so that players of average skill will generally keep most of their ships somewhere between insubordinate and loyal. Unfortunately, that's a very difficult thing to do without a significant amount of data to analyze, so it's bound to be off. Different playstyles also complicate this. Another related problem is that loyalty is harder to maintain early game due to smaller battles yielding less XP. This is something I want to address at some point, but I haven't settled on a solution yet.
Loyalty reduction can also be reduced or even negated under the right circumstances. Weak ships that participate in battles involving strong opponents are far less likely to lose loyalty, as well as ships with any hullmod or skill that reduces crew casualties (e.g. Reiniforced Bukheads, Damage Control, Containment Procedures)
I know all that doesn't address every point you brought up in spite of being rather longwinded and rambley, but I do appreciate you taking the time to give feedback, and I'll keep it in mind when I consider future changes 
If you couldn't just swap officers to reset to indifferent, I think that system would work a lot better. Good to know that preventing crew loses also leads to better loyalty. My personal suggestion would be to cut the low loyalty values entirely. Have the baseline be the minimum. Then have loyalty be something like a kill streak, it rewards players for keeping their ships alive and not shuffling around their officers. D-mods and repair costs are already punishment enough for loses. Say:
Untested (baseline): The crew is still unsure about their officer and is in a 'breaking in' period for their new posting. -10% Peek operating time.
Indifferent: The crew has no strong feelings about their officer, but work together well enough. No effects.
Warm: The crew and their officer have worked out their kinks and now work together well, their special skills can now start to shine. -10% CR decay, +small ship traits.
Confident: Same as before
Loyal: Same as before
Untested is usually cleared after one battle and ships will generally stay at indifferent for extended periods of time. While warm, confident, and loyal all have relatively similar experience values separating them.