I wouldn't use a dremel for drilling, it has far too high rpms, even on the adjustable speed and low speed ones. They tend to catch and jump out of the hole too easily and you risk damaging the mini.
A cordless hand drill works much better. I have a Black and Decker 12 Volt drill I used to drill out the bottoms of all my Minbari fleet for the Ninja Magic magnetic base adaptors. It has multiple torque settings to use it for a power driver and also a single setting for drilling. It's good because it is a low speed drill and works perfectly for drilling out the minis. I started with a 1/8" bit to drill out the main part of the hole for the larger portion of the base adapter's pin and a 1/16" bit to do the "countersink" hole for the smaller portion of the adapter's pin. I did this on all the ships except the Tarotha as they are so thin I couldn't do both holes without drilling through the top of the mini. On them I only did the 1/16" holes as they are small enough to not break the pin on the base adapter.
I agree on the pin vise, for the type of work you are doing here it's not a good investment. It's really only good for working on other types of minis like humanoids and monsters where you need extra control over where you are drilling. Using the pin vise to drill out all those ships will make your hand very sore after about the fourth or fifth ship, or maybe my knuckles are just worn out from working on far to many minis in my lifetime.