How long, and how hard, for Why? Again?
 
You weren't asking me, but I enjoy making and doing things myself, even if that requires more time, money and effort.  Even if some folks consider it bodgery (by which I assume you mean cobbling something together, not chair-making). 
And, sometimes, it's actually less effort and money to just make or do something.  For example, I spent quite some time and effort trying to find disc set spanners for an AyA 4/53 that quite firing in one barrel.  I finally gave up and made my own. Turned out not to be a firing pin issue as expected, and I'm glad I didn't send it all the way to New England (AyA's US repair site) to figure that out.   In fact, the problem was floating metal from a poor repair of a broken internal part, undoubtedly by the same smith who buggered the screws.  After I found the problem, I was quoted about $400 plus shipping, FFL, etc by my nearest 'qualified' gun smith to repair.   Instead, I ordered a replacement part for $12 plus shipping and fixed the gun myself (following the advice on how to repair it that I got from said gunsmith-- they were very helfpul).  It was my first gunsmithing project.  I ultimately saved a lot of money, and also learned a ton in the process. 
Here's what I found under the hood:

As to the original question of "how?" not "if?", I don't have even a fraction of Mr Flynn's experience, and I suspect his answer or something similar is best.
What I did, for what it's worth, is use a small belt grinder to fit the drivers I used.  I started with a set of Grace drivers that turned out to be too thick, just like your Brownell's bits.  Would have been cheaper to use old junk drivers I had laying around I guess.
I also made new handles on the lathe, but that was just for the fun of it. The only disadvantage I see to that is that I don't have the option of chucking them up in the press, which would be great.   
Here's a picture of some of mine.   Obviously a waste of time to make nice handles, etc except for the aesthetics and fun of making something on the lathe. 
