How to deal with "weird" phase plots in bode diagram when designing a controller
I'm a bit puzzled with your Bode plot, here's what I get with your transfer function and Matlab 2019b. My phase starts at almost -180 degrees while yours start at 0 degree. Is it possible that you've made a mistake somewhere in your analysis?

Your transfer function is a bit complex, you could simplify it by removing the fast poles and zeroes. For example, you have 2 fast poles at -1714 and -516 and a fast zero at -1088. You can remove the 2 fast poles and the fast zero to simplify your transfer function. This will make your analysis easier.
Secondly, I think the rule-of-thumb formulae you use for the cross-over frequency is only valid when your open loop system has a low-pass characteristic. Your system has a band-pass characteristic.