Like Brian Ward, the author of Galoototron, I am using a really thick piece of Beech for my face vice. He used an expansion bit with his brace to layout the circle for the 1 3/4" hole, and finished it up with a router plane. I think Brian voiced many people's opinion about these infamous tools when he said, "Now, those bits are not known to be terribly good even in soft woods, much less something like beech."
This statement got me to thinking about Aldren A. Watson's book "Hand Tools: Their Ways and Workings". I vaguely remembered that he discusses the expansion bit for the brace. Essentially he says the expansion bit only has one cutting blade, so there is nothing to support the other half of the cut, like a typical brace bit with two cutting blades. This can make it difficult to drill straight, as the brace becomes unbalanced and wants to move all over the place.
First, one should really tighten the screw on the adjuster mechanism tight, otherwise the hole will get bigger as you bore (don't ask me how I know this). Please do this safely and away from your hands. I put the bit on my bench when I foresaw blood gushing out of my wrist.
The trick with this cut is to use a lot of downward pressure, and use the ratchet mechanism on the brace. Only make about 1/8 of a turn before ratcheting the brace back to your starting point. I found it easiest to pull the handle a few inches with my right hand before starting over.
This worked great! My cut was perfect. The inside of the hole was pretty ragged, but it could easily be cleaned up any number of ways. The bit worked good and took nice big shavings out of the scrap of beech I was practicing on.
A video is worth a thousand pictures, so here is the technique in action:
(notice the cool bench dogs in action)
The down side of this bit is that I'm pretty sure I don't want to drill a deep hole with this bit. The deeper I went, the harder it got. Perhaps a 14" sweep would help. Also, for an accurately sized hole, one must make a few test cuts. It took me six tries to get exactly 1 3/4" diameter.
However, I think for occasional use (really, how often do you make a hole bigger than an inch, anyway) this bit is a valid option. On those rare occasions when you need a big hole, you will have a way to do it.