Hi MikeW,
Your question is not stupid at all.
I studied the amp's manual before writing this. What I know from my own experience is that 5751 will not make enough difference in gain for what you want to do. But if you want to try one, get a GE short grayplate, it won't break your bank and it has a wonderful tone. There is something to be said for twiddling knobs, but that can only help so much. Changing the gain in the preamp tubes also changes the way that the amp responds to a player in a way that knob tweaking can't.
Ebay is a great source for the tubes I am recommending, I get nearly all of my tubes there, and have a couple hundred or more in my collection, and my friends whose amps I have voiced from my vintage old stock collection prefer their tones after I get done...by far... sometimes you get lemons, but the more experience one gets buying there, the less often that happens.
Change out only one tube at a time. 12at7, cv4024, or 6201 (all the same same tube gain type) will do more of what you want. Put the 12at7's in V2, V1, and V4. That will cover most of the gain stages in the preamp and also cover the phase inverter tube as well. The phase inverter needs to have matched sections to work the best and give the best tone. The other positions don't require matched sections.
Start with v2, that oddly is where the first gain stages are, then if that is not enough stick a 12at7 in V1, that is where the next gain stages are. Newysurfer is right on that one. Finally, if that is not enough, stick a 12at7 in the phase inverter slot, (balanced sections). That will go a long way to taming the amp like you want, and you probably will still be able to get plenty dirty for your purposes if you want.
I love the Mullard cv4024, that tube is the one to get in balanced sections for your phase splitter slot, you can find them from serious tube dealers on ebay, but expect to pay more for one, they often go for over 40 bucks each. And yes, for the kind of money you spent on that amp it is a good idea to have some exceptioanally nice tubes, Mesa amps give back very well when you pimp them out. Other great choices are the Raytheon 12at7 blackplate, either the US Navy version with the yellow print and the "anchor" symbols, or the Raytheon red print triple mica blackplate, my all time fave. Other choices include Tungsol grayplate 12at7, and Sylvania triple mica 12at7 blackplate. All these are wonderful sounding, and most vintage 12at7's are often gotten for relatively dirt cheap.
Finally, Albert Einstein is credited with the saying that "Great spirits have always encountered violent opposition from mediocre minds..."