Ya know...it's not that bad...
You're essentially 25% of the way around the circumference.
you stated that you broke bits. Is it safe to say that the dearly departed were the pilot-hole bits (center)? erm... I guess it would have to be.
If so, it is due to excessive lateral pressure .
If you have some C-clamps and a work table you could use some plywood and 2x4's to brace the panel whilst accounting for the punch-through. Being able to brace the work without having to use your hands or feet will allow you to focus on the cut, and not worry about the panel that is being cut.
Once you have the work fully secured (the panel is held securely in place by itself), start with the hole saw again. I think that you must have been standing on the left-side (orientation of pict) and the cut was forming from the 12 o'clock postion to the 3 o'clock position. That is the nature of the torque and the inclination that the holesaw will tend toward (for right-handed peeps).... but I am speculating.
The object is to keep the teeth of the blade in uniform contact as it travels around the area that you are cutting. This may require you to tilt the drill and the bit to the left by a degree or so...
If you do try to salvage the panel yourself, use some oil to lubricate the contact surfaces. Take your time, and stop periodically. Drilling these types of holes can be fatiguing and your grip and steadyness will falter.... that's generally when the the blade will disengage and skip.
Additionally the drill will need to cool off a little so that you do not burn it out.
...or you could take it to a machine shop. They should be able to whip it out in no time at all.
okay... I'll shut up now..