Use the appropriately larger drill bit, in a drill press, and clamp the panel down to a piece of wood on the press tray, using either a plastic clamp or a metal clamp with a small piece of cardboard under the foot, to avoid scratches.
Reamers make beveled holes, so one side of the panel will have a slightly larger opening than the other. Also, reaming by hand in steel generally results in star shaped holes rather than round. This happens with aluminum also, depending on the grade. The biggest mistake people making reaming holes is applying too much pressure. Like with all cutting tools let the cutting surface do the work.
If you do not own a drill press (table top $99 model is fine), see if one of your friends have access to one. You can enlarge holes with a hand drill, but enlarging holes in metal affords you the risk of the larger bit "biting" and you can seriously injure your wrists this way. Also, the bit *will* walk a little bit.
My floor-standing Delta drill press is probably my most used machine, but for this purpose you really don't need anything that big and massive. You just need the stability of holding the bit at true vertical. You probably can even rent one for what it would cost to buy a reamer, the reamer grip, and make nice round holes!
You asked about punching... there are three types. The cheap type you just hold where you want to make the hole, and beat it with a hammer. It only works on thin material (like your panel), but the drawback is it will warp the panel around the hole.
The right way to do it is the bolt-through punch, which has a bottom piece, and a top piece, and a hardened bolt that goes through the center of the two pieces, and the panel. Then with a breaker bar or an impact gun, you tighten it and it pierces the panel. That's how I make panels that contain oddly shaped openings, for RS232, RS422, VGA type connectors, the d-sub connectors. I have a set of punches for those. And they weren't cheap.
The only real way to punch without damaging a thin panel is
a hydraulic punch, and for 4-6 holes, forget it. Drilling is by far easier and less costly.