use a reamer only ! it won't grab and snap like a drill will.
i don't know what size hole you have to start with, but a reamer is designed to only enlarge around .010 [ten thousandths] above the drilled hole size. you will more than likely, have to buy a couple of them to arrive at your desired hole size. use plenty of lube, relieve the hole often to clear the chips, and take your time.
reamers come in extended reach in virtually all sizes, so you don't need to settle for a shorty.
try mcmaster-carr for your needs, or possibly the bag.
the only thing to watch for before you start, use something like a coat hanger or welding rod, and run through the hole to make sure there is nothing obstructing the hole. i have see all kinds of "stuff" [especially in cast holes] hiding in long holes that still allowed the hole to function as designed, although not at 100%, such as chunks of broken tooling and casting boogers. both of which can shatter quality tooling upon contact. you shouldn't find anything, but you never know.