In my games, I usually use a simple 2d10-equivalent mechanism when resolving success or failure.  However, I'd like to come up with a reasonable alternative to this for handling cases where the question isn't really "can you succeed?", but rather "how long will it take for you to get it right?"  Ideally, this would be a system that gamists wouldn't be averse to using in place of making a series of success rolls until one succeeds, tallying up the rolls, and basing the time taken on the number of rolls made (I believe that this is called "whiffing"?).  More generally, it would be nice to have a mechanism for condensing a bunch of rolls down into a single roll that roughly approximates the same outcome. 

Any suggestions for how to go about doing this?

Baseline time for completion could be modified according to a target number. (11?) Every x you roll over or under (your choice on which is good/bad, there's reasons to use both) is less or more time to complete. The baseline dictates what the steps are, so maybe a "5 round" baseline is one round per two over/under (11, 13, 15, 17, 19) and one hour is five minutes per over/under (11, 12, 13...20)

Wow, makes it hard with 2D10, because of the bellcurve. If it were linear randomness it's pretty straightforward - ie, if it has 50% chance, it takes 2 attempts, etc. Indeed D&D 3+ covered this with the take ten and take twenty rules.

Instead of looking at that as a bad thing, look at it as plausible. If something takes 10 minutes to do, you might be able to get it done in 9-11 minutes regularly, but much more rarely would you either be much quicker or slower, and certainly it might be very rare for you to get it done in as few as 6 minutes or as many as 14.

Bell curves are good for some things, like making it likely that things will end up in the middle most of the time.