Welcome to your first Deathmarch(tm)!
I think everyone has to go through at least one to experience what it is.
20+ hours overtime/week 3-4 weeks leading up to a major release, most would consider fairly normal, or at least acceptable. Personally, I look at any overtime as a failure in project management but a certain degree of estimation-error is often inevitable towards the end of a complicated release-cycle.
20+ hours/week of overtime over a sustained period (months) is not an estimation-error, that is a systemic fault. Either you have weak steering, unable to prevent substantial scope creep or your development-process and architecture is so bad that you can't produce effort estimations with any level of accuracy. Or you have particularly cynical management that simply thinks running people over the edge and re-hiring after each project is easier than building a working development department. That is rare though.
In my experience, the only way to break out of the deathmarch-cycle is a dramatic de-scoping of the current effort. Few companies have the fortitude, resources and humility to actually do this and many will simply let it run it's course. For a small company, it can often end in financial ruin. For larger companies, they may succeed in pushing through, but a lot of talented people will quit, the product or project will be considerably more expensive than anticipated with lower quality which will take even more time to fix. Probably some middle-management fall-guys will get the axe.
If you manage to get a scope-revision in place, that's a hard and real process to determine:
- How much longer can the team sustain a positive output and
- What can realistically be accomplished with a minimum acceptable level of quality in that time
Assuming this can be done, once the release is out then it's imperative to really get to the bottom of the systemic problems that led you there, or they will just keep reappearing.
- Why can't you keep control of the scope? Maybe you need to look at tighter control and prioritization, or maybe smaller, iterative releases with more frequent re-prioritization? Maybe you need a more formal structure with steering committees and stronger project management?
- Why are the expectations not in line with your final product?
- What is preventing you from producing accurate effort estimations?
- Are your ambitions such that you actually need to hire more people?
In closing I can tell you that no amount of perks or motivators can keep people satisfied over sustained periods of time under these conditions. There is ample research on the subject, for example you can take a look at Herzberg's Two-factor theory. Offering motivators (extra overtime-pay, additional perks, teambuilding, etc.) will make people pump overtime for a limited period of time. However, decent working-hours overall is a firm hygiene-factor for almost everyone.
So to answer both your questions: you can't. Stress, burn-outs and illness are physiological manifestations of what happens when you're overworked in a constant high-pressure situation. It will happen to everyone eventually. Low morale and performance are the psychological manifestations of the same problem, equally inevitable.