Thanks for all the replies, very helpful. It seems the problem is the drill and drill bit, not the packing tape. And I was using too large a drill bit.
All has changed. I bought a roll of blue tape and a new Pegas scroll saw. (I might have the order of importance reversed.)
Bottom feeding, or top feeding for that matter, are much easier with the Pegas. So I can use a smaller, and hopefully sharper, drill bit. So maybe it won't matter if I do not change the speed on my drill press.
Did I mention I got a new Pegas today! I already love it.
BTW, I love this SSV. You guys are great!