A "matrix" is just a digital mix of two or more sources. Like, say getting two recordings, one from the soundboard and one from mics in the audience and mix them together through a computer program later (or getting an expensive multichannel recorder, but that is probably not the way you want to go), thats a matrix. Here is a relatively simple explanation:
http://www.shoey.com/dat/matrix.aspIts a little wordy, but basically says: "Three options for recording: 1, straight through the soundboard (clean sound, no audience ambiance), 2, from mics in the audience (can be a muddy recording), 3, get both and mix them together later. Option 3 is best, but can be tough because of a very small difference in timing when the sound (the digital 1s and 0s) is recorded both through SBD (soundboard) and the audience mics. (for a comedy show this might not be such a problem since its only 1000ths of seconds off, but I don't know how crucial the timed laughter is supposed to be.) BUT, there are programs to correct this issue in post production so not to worry."
To respond to the link of quality you're looking for, that sounds like it'll be expensive if you're looking for an audience mic rig (which 99 % of people here use) BUT I would hazard to guess that recording didn't come for an audience placed mic setup.
THAT BEING SAID THOUGH, how do you like the recordings your mic now gets? I'd suggest trying different placements of that pointed somehow so it'll pick up the best sounding laughter and see how you like the clarity of the laughter. If you are happy with how the laughs sound, then look into a small digital recorder (the ones I mentioned before are a little pricey for your said budget but are the popular "affordable" ones in this hobby, just google "compact portable digital recorder" and look over reviews.) With the digital recorder you can record through the soundboard which, if mixed (as in the mixture of bass/treble ect... coming through the SBD) are set correctly, will sound perfect, if its the same mix that comes out the PA it will likely sound great too (I don't know how sound guys mix PA systems to sound best in a club with vocals only, for bands the mix is different than what would sound best on a home system, but you might not have that problem.)
Now you're all set and just have to figure out some computer programs that allow you to mix the recordings and you have a pretty darn good product. HA, reading this all back it seems slightly overwhelming. Its a lot of work, especially on the computer end, but if you're interested in it, it can be a fun project. But if you're not really too into it after trying, that's why people pay for this type of work.
Being in San Diego, you could try to post in the "Team SoCal" page on the team boards to see if anyone wants to come out and possibly tape the show. (not too many people have been reading this thread) I'd just say subtly, "that you're a comedian and looking to get good recordings of gigs. If anyone wants to come to a show I'd be more than happy, and if you also wanted to give me a couple taping tips as well, I'd appreciate it, if not it'll be a good night of comedy either way." If anything, its just free advertising.