Hmm. I've never thought about changing string gauges in terms of changing speed...
...probably because I've done this, and not really noticed a chance, I'm going to guess no, you'll see no change in speed. What you WILL see is a change in stability - as you've noticed, youi'll have a harder time knocking them out of tune.
They'll sound different too - not better, not worse, just different. A little darker and more compressed.
The one area where you MAY see an increase in speed is, if you tend to really dig in with your pick, such that your pick tends to get "hung up" on the string, it becomes VERY hard to do this with heavy strings and heavy picks because they have so little give to them. So, short term this may actually decrease your speed - long term, it'll force you to develop better picking habits, which will probably help you speed up.
If you're curious, do it. You may like it, you may not, but at least you'll learn from it, and strings are pretty cheap so you'll be out like $10 plus the time it takes you to set your guitar up.
No need to change your pick BTW - if you like it, stick with it.