I have the same Z problem and my best solution is the same set of R8 collets as RJSakowski. All my drill bits are screw length instead of the usual jobber length.
Believe me, I hear you. Saying "Money is tight", is an extreme understatement, however. I have been out of work for over two years, and my new company is not yet bringing in any revenue. I have to make do with good enough and cut every corner that doesn't significantly impact work quality in any important area. A large set of quality R8 collets is pretty much out of the question. Most of my work does not require more than 0.005" concentricity, if that. When it does, I take extra care, or else bite the bullet and buy a more precise solution.
I am aware of the best solution, but I simply cannot afford it. I do have some stubby drills, as well as some 6" and 12". I also have some custom made drills in lengths that match my tap wrench for tapping. It allows me to drill and tap without moving the drill table, which not only ruins the registration, it is also a pain in the patootie. Obviously, tapping otherations on this mill are not practical.
With that set of collets and drill bits I’ve not been stumped yet. Using my drill chuck is not really an option as I don’t want to lose registration when raising and lowering the mill head.
Process organization can make a big difference. Whenever possible, I complete all milling operations for a particular target orientation first, and then do the drilling before moving the piece or the fixture setup.
Personally I’ve never run into hex shank drill bits that are as good as my regular drill bits, but I can’t say I was looking as I don’t even think about using them for more than wood etc.
I've done some pretty accurate woodwork, actually, although nothing like 0.0001", of course. On the other hand, many of my projects don't require even woodworking accuracy. Indeed, I just milled a piece for my lathe where I didn't even measure the piece. I put it in the vice, leveled it by eye, and cut off about 1/8" without even touching off on the piece. Precision was not required, so I didn't bother to take the time. By the same token, I am working on a press fit bearing later today or tomorrow. Obviously, that will need to be within a few tenths. I will be taking my time and doing my best to make up for the limitations of my little lathe. Needless to say, I won't be relying on a drill bit at all for the sizing, let alone a cheap hex shank bit.
Let me give a common example. In a situation, very frequently encountered, where I will be boring a large hole either on the lathe or the mill, I will typically start with a center drill, then move to small drill bits in ever increasing diameter. The hole size of these intermediate operations is completely flexible. If the drill bores 5 or 6 thousandths oversize, who cares? Even if it is off-center a bit, the boring bar or boring head will take care of it. Being able to change those bits quickly and easily is paramount, however.
I am going to give it a try. If it turns out to be too much of a time suck, or produces too poor quality output, I will move to a more expensive solution.