I can't see what the problem is for drilling top-dead-center. It isn't magic. If you have the barrel already on the gun, which IMO is infinitely better than pressing on a fully-assembled barrel, then all you need to do is clamp it down on your drill press table so the receiver itself provides alignment. Mark/scratch/file the spot, give it a good center punch, and double-check with Eyeball 1.0 to confirm it is at TDC. Drill. Done. Go slow, of course, and don't force it. HIGHLY RECOMMENDED to use a drill press or something else to hold the bit, otherwise when the bit torques, and it will, you'll snap off that bit. I for one have never done that but I've dug out enough broken bits to know it doesn't pay to be "that guy" that digs out that bit.
Resting's recommendation is spot-on. It isn't that hard to hammer something out of a .22 sized barrel. A hammer and an ample supply of cleaning rods and you're all set.
It is NOT a bad idea to push something into the hole - bullet, brass cleaning rod, wooden dowel, anything - because if you have ever drilled metal you'll understand that the bottom of an unsupported hole will leave a burr that extends past the bore you just drilled. In other words, into the barrel. On the 45 win mag I decided to try drilling without a support just to see, and sure enough the drill raised a burr in the barrel even when going slow. Sharp bits help reduce this. Much easier to deburr a .45 sized barrel, but still a PITA.
If you don't support the hole, have fun getting those burrs out. You'll fiddle with cleaning rods, the drill bit, and a paper clip or some other thin and bendy thing to try to break off those burrs. On an open hole it is no problem, you either counter-bore the bottom of the hole or use a deburring tool. But you simply can't do it in a long tube.
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