I absolutely thing you need a rest day. I also don't do a day where I just sit around and do nothing...I'm still active, but your level of intensity is quite high and your body truly needs a break to recover especially if you want to prevent injuries.
First goal: under 180:
Second goal: 175 or below:
Third goal: 168 (no longer overweight):
Fourth goal: 160 or below:
Final goal: 145-155 (not sure if this will ever happen):