TBH I do have a proper wood lathe (of course), but it's not set up for this miniature crap. I don't think a man's supposed to have a mini lathe and turn pens for all his friends until he's over 58 yrs old or something. (Yeah, there's a rule like that, I just don't remember exactly). If I'm actually still interested in this in a couple days, I'll be setting up the proper lathe (pro'ly need a special chuck, and a special tool rest at least).
I too have a mini lathe for wood, and it can handle some pretty large blanks. I would need to get a new chuck for the smaller stuff, and new tools as well as a new rest. CATastrophe and I have talked about it some, but never made the plunge. The problem with wood drip tips is keeping them from swelling with the moisture, and putting a finish on them that will not cause harm. I am thinking about getting some of that truestone and experimenting with turning that material. And, since I am over 58, I am safe from the rule.