What are you using the JLJ for? Virtual On? Bangai-O?
Neither. I play
Sensible World of Soccer "96/"97 (an old Amiga favourite) online somewhat competitively. It plays a lot like a hybrid between a 2D beat'em up and a shmup, despite being a soccer game.
I go up against people who use keyboards or keypads, so I have to make up for the gap in input speed (the faster you are, the longer the ball will travel and spin, etc.) by using 2 hands (= 2 joysticks) simultaneously since the gameplay requires forward->backward and left->right motions for pretty much everything (shoots and long passes especially as you aim, fire and then raise the ball and/or curl it by pulling the stick back and then pushing left or right depending on direction, all of which has to be executed faster than a FADC shoryuken, if you get what I mean).
I'm thinking of making a dual stick panel for things like that, so I'm interested in what you come up with.
JLJ-PL2-V are most likely your best bet if you're going to implement unmodded, stock joysticks, lots of VOOT passionate fans use them in their sticks. They're very responsive and sturdy.
The biggest thing that would make that stick feel like it has a long engage/throw is that the handle/grip extends so far from the pivot point, and you have to hold at the top of it to use the buttons, creating a long lever arm. If you could mod the shaft and grip to be shorter, that would make a big difference.
Unfortunately that's not an option, I grew up with Quickshot (cheapo and plastic-y) 16-bit era trigger joysticks and I have never been able to get the same feel from short ball-tops.
check out the last link in my signature for an example of the latter.
That's one interesting mod, I might try it out on a JLF and add into the mix a Toodles' Spark Optical Joystick sensors kit for good measure. That'd make one helluva replacement for my old LS-32 as the off-hand lever on my control panel.
As for using other Joysticks, I don't know about native-top fire models, but for the shortest throw you're going to want a JLF with my mod or a Seimitsu LS-33. Maybe you could then mod a normal balltop to put a button on top. There are hollow shafts available for the JLF to run the wires, and I think for the LS-33.
Sounds like you're not impressed with the throw/engage ratings like those at Slagcoin? Check out Kowal's pages for actual measurements (apply Google translate where necessary). Throw and engage are physically measurable distances, the numbers don't lie.
http://www.kowal.itcom.pl/ArcadeParts_pliki/joySLS33.htm
Problem is, I do own a LS-33 and its throw is not that amazingly short (in comparison, the JLJ seems to have a much shorter throw and definitely has a shorter engage, despite the difference in size, no kidding, no chart has ever taken the JLJ in consideration tho)...also the stick feels kinda sloppy (although I've never gotten around replacing the spring with a tighter one), same goes for the LS-32, so I really don't know whether I should trust said charts (I knew about Kowal's too, he's the one stating that the Happ Top Fire has a long throw) or not, things just don't quite add up as they should imho.
How do they even measure throw, engagement and stuff, exactly?