If you’re willing to use an external controller to change your presets, you can open up all kinds of possibilites!
You don’t have to use SYSEX messages -
MIDI program change messages are MUCH easier to use (less cryptic!), and should do exactly what you want it to do.
You could set up a bunch of Program Change controls that would let you jump directly to any preset on-the-fly, with no menu diving required.
(Note that if you want to actually load in new presets to the LP’s memory, you WOULD need to use a SYSEX app and messages, but that’s not necessarily something you would want to try “on the fly”, since the LP is essentially “offline” until the transfer successfully completes).
The iPad makes a GREAT MIDI controller for stuff like this ~
I use an app called MIDI Designer, which lets you, fairly easily, create a custom MIDI control surface to do exactly what you want to do!
You will need some sort of MIDI interface between the iPad and your LP; if you aren’t planning on putting a computer in the mix, an interface like the iConnect Mio should work great for you, and fairly inexpensively.
You could setup a “Preset Select” page using MIDI Designer, with as as many dedicated preset buttons as you want, each one sending a Program Change MIDI message that points to a specific preset position in the LP. These would be setup using the “radio button group” feature then ensures only one button in the group is active at a time, so no conflicting MIDI commands are being sent to your gear. Once these are setup (would actually only take a few minutes to do!), all you would have to do is tap the desired button, and your preset is instantly loaded and ready to play.
BTW -
There’s a few of us on this forum that have made custom MIDI Designer apps to use for Moog gear.
If you check out the MIDI Designer web site, you’ll find apps for the MoogerFooger Delay, Animoog, and Filtatron, as well as a controller I built that lets you access all the “behind the scenes” settings on the Little and Slim Phatty’s from just two touch screens. 
Note you don’t need anything to use these apps other than your installation of MIDI Designer:
http://mididesigner.com/community/
http://mididesigner.com/qa/1910
Good luck -
Keep us posted!!
Randy