Get a new drill bit.
My chart says that 11/32 corresponds to 8.75mm - 3/4mm would be a lot of sanding. The real risk is that if the hole is too small, inserting the tube will squeeze out most of the glue and starve the joint. If the tube becomes loose while turning, you have a disaster on your hands.
Chinese-made carbon steel bits are very inexpensive; I picked up a 117 bit set on sale at Harbor Freight that includes fractional, numbered and letter-size bits that I reserve exclusively for wood. That way, they last longer without dulling and the need for resharpening. You can also find similar sets in high speed steel and also the fancy titanium-plated steel, but I don't thing either is necessary if you are only going to use them in wood. I know there are far better bits out there, but these are good enough for my purpose - drilling holes in wood.
