Funny you should ask that....
I just filled up a UL size spinning reel for the upcoming ice fishing season. I wanted to use 4 lb. Fireline Crystal, which I only had a partial spool of. I figured the best way to figure out exactly how much backing I needed was to put the Fireline on first, then fill the spool with backing until it was perfectly full, then take all the line off and put it back on with the backing first. Clever, huh?
Well, I put on the Fireline, then filled the spool the rest of the way with 6lb. test mono. Good. Then I thought about what I'd transfer the line to... another reel? ...a large empty spool? Then it hit me. If I take it off the new reel and put it on another one, or a empty spool, it would still come OFF the other reel or spool with the Fireline first and backing last! Doh!!!
I ended up outside in the yard, walking out line until the reel was empty so I could cut it, then go back to the other end and put it back on. Thank God it was a low-capacity ultralight reel or I would have had quite a project.
Unless, of course, there is an obvious and easy way to do this that I didn't think of....
Anyway, to the OP, I would use a similar or slightly stronger test line for the backing. The odds of a fish getting you down into the backing is pretty slim, so it probably isn't too critical what you use. Very slim odds you'll be casting far enough to get into, also. As for exactly how much to use, I would advise against using my clever method.
Tight lines,
Bob