OK! I finally got this figured out. I'll share my solution here should anyone have problems setting up their MIDI controller to control an HX Effects.
I use a Decibel 11 Switch Doctor. I LOVE it. It has two CC banks, A and B. Under normal operation, a value of 000 is sent to a MIDI device when a switch is turned off. If you'd like to set up your device to switch Snapshots, and it operates similar to the Switch Doctor, you'll have to set it up to ONLY SEND ON commands to the HX Effects in order to create presets on your MIDI controller that switch Snapshots. The problem will then be that you'll have no way to get to Snapshot 1 since value 000 on a CC number is sent when a switch is off and you're now only sending ON commands. To adjust for this, on your second bank, in my case, CCB, create a CC of number 69 and you can leave the value at 127 for when it is switched on. This won't do anything on the HX effects, it's just a dummy value that you turn in order to avoid sending a value of 000 to the HX Effects that will automatically switch to Snapshot 1. So basically you'll want this switch on whenever you want to create a preset with Snapshot 2, 3, or 4 on your MIDI device.
This is also why whenever I tried to create a tuner preset on my MIDI controller, it kept switching the tuner on and off. The tuner by default is set up to switch on or off when receiving CC number 68 and any value. It's really sort of any annoying setup and I'm bummed Line6 chose to set it up this way. On the M series devices, you could choose a CC value to turn the tuner on or off, instead of all or nothing. So, I set up my tuner on the same bank as the ONLY SEND ON snapshots.
Ideally, it seems to me it would've made more sense to set up the Snapshots on their own separate CC numbers with a value to turn them on and off. Or at a minimum, not use value 000 for Snapshot 1. But that said, I managed to figure it out, even though it's not pretty.
Anyway, should anyone have issues setting up their MIDI controller with an HX Effects, or their Decibel 11 with the HX Effects, I hope this helps. :)