Sometimes when I'm playing jigs at full throttle I notice I get the E string accidentally and it creates a pleasing, brief "brrrp" sound. I'm assuming this is what the pros refer to as "cross picking". How would I go about creating this purposefully? I can't seem to recreate it unless it's accidental and I'm in a hurry.
If you get Gerry O'Connor's DVD he discusses crosspicking. I suspect that what you are doing is not really crosspicking as it does not involve three strings. I think I do the same thing under those circumstances and I just let it happen. Everytime I try to crosspick (the way Jesse McReynolds does) it is a disaster as I have not practiced enough and I don't relax enough to do it effortlessly.
Get the GO'C DVD and see if that is what you want.
Note the interesting evidence of power of authority in this issue. Mandolin players are following their hero Jesse McReynolds who crospicked with the pattern DUU (3rd string down, 1st string up, 2nd string up, like the backward roll of fingerpicking players) while bluegrass guitar players follow the other hero George Shuffler, who picked his guitar with DDU pattern (3rd string down, 2nd string down, 1st string up, like the forward roll). Note both these heroes played together in the early 50'.
(And there is the other authority - Steve Kaufman - who says you have to keep DUDU pattern even if you cross pick. Both camps (sweeping and DUDU) show the pros of their approaches. It is similar to the DUD DUD and DUD UDU issue of jig pattern).
I doubt that what you're doing is true cross-picking, as that is an intentional technique on three strings, while you seem to be accidentally sounding a string by mistake.
There is a mandolin technique called stolen tremolo where one string is trembled as usual but a quick stroke is made to an adjoining string. That sounds more similar what you're doing. To get an idea of stollen tremolo, check out Evan Marshall's Mandolin Magic. You think crosspicking is cool? Wait to you hear this!
You don't have to be loud. Just be so good that everybody shuts up and listens.