My drill press has a 4" spindle travel. ( Porter cable drill press - $299 at Lowes-I LOVE IT!!). Another option, IF YOU HAD A JAW CHUCK would be to just slide the entire tailstock assembly into the blank (with a bit and drill chuck inserted obviously). Other then those two options, I dont know. I will say, shy of the lathe, that drill press was one of the best things I have bought as I used to have the sam problem with the craftsman I had. Plus if you figure on sellling what you have after buying a new one the cost wouldnt be that bad. It is already a VERY reasonably priced unit for what you are going to get in my opinion.
Jonathan