What does potential PhD adviser want to see from a candidate that is applying for a second PhD/restarting a PhD?
You should continue to apply for postdoc and industry positions and not consider quitting or applying for a second PhD.  The things you've described here are not atypical for someone working on a PhD.  It is expected you will work independently and in a self-guided fashion.  As a PI, I have little sympathy for a student who runs out of RA funding and now has to TA.  Being a TA is valuable job experience that you should be proud of and having an RA position is a luxury to all graduate students that you should not play off so lightly (it is very difficult to get soft money in grant funds to support RA's in the first place).  Your description of working 80 hours per week on holidays and weekends sounds very typical of a student trying to finish their PhD (I did that for many months leading up to graduation).  Going back for a second PhD would not necessarily increase your chance of success in finding a postdoc or industry position.  It sounds like your are simply discouraged by your situation and have not searched for positions long enough.  Keep at it and stay positive.  Finish your current PhD.