ha, just thought of a bo-janged backwoods way to build a coring bit...
first, go find yourself a beer in a CAN and drink it.
use some scissors or whatever, and sacrifice the can to give you some nice thin sheet aluminium. now find yourself a 1/2" piece of dowel (could use some of your pvc, but best if its actually a tad smaller diameter) wrap some of your aluminum around the dowel, extend the aluminium past the tip so that the aluminium is flat at the bottom hollow end that sticks past the dowel.
secure aluminium to dowel with a handy hose clamp or two... chuck in drillpress or drill
(carefully shave down the dowel if your chuck cant handle the dowel...)
(or even better: use a drill bit as the dowel!)
presto, a corer!
i'd worry a bit about the can aluminium being too flimsy (our cans have a thicker wall up here in Canuckistan), but you get the idea. id be tempted to just extend the "blade" a 1/4" past the dowel so its nice and stiff, then core in short sections... either using a knife to pry/shave/pop out the newly drilled sections, or extending the blade bit by bit...
drill bits and even hole saws just have such a high chance of tearing the rubber, i really think going to the trouble of coring is going to give you your best result.
you could buy a 1/2 coring bit... we use them sometimes for punching EMT through concrete walls, but thats going to be pricey, one can of beer and a hose clamp is cheap...