Ground Control is very capable and would do what you want, but it is enormous & expensive. If you have other MIDI gear, could be worth it - I would say it's overkill for just the SYN-2s.
I also have the stock Synergy R5 switch, which is built like a tank, works great for a single SYN-2. It does not have MIDI in port on it - there's no way to program a single R5 to control multiple SYN-2s, or even chain 2 of them together- would need to run 2 different MIDI cables running one to each SYN-2. 2 R5s would still be $150-170 cheaper than a Ground Control & smaller.
If you want a smaller & less expensive option, look at Disaster Area Designs - I got a MIDI Baby 3 to use with my SYN-2, Mesa TC-50 combo & a several MIDI Pedals. It is much smaller, the interface is really flexible and easy to program, you can program each button to do 3 different things (press, short hold, long hold), including cycle through channels on SYN-2 with a single button. It's also expandable, you can add 1 or additional 2-button external switches (no LED for the external switches). There is supposedly a 6 button Midi Baby in the works also.
https://www.disasterareaamps.com/shop/midi-baby-3
I also use MIDI functionality of my Line 6 HX Effects to select specific channels/bypass on my SYN-2 for individual presets. The HX Effects is much clunkier to change SYN-2 channels on the fly within an individual preset, which is why I got the MB3- both are connected, so I can still use presets on the HX Effects linked to a SYN-2 channel & have the MB3 to switch on the fly.
I wish Synergy had included an "un-bypass" command for the SYN-2 that put the unit back to whatever channel was last selected. Would make it much friendlier for 3rd party general MIDI controllers.
EDIT: forgot to add, with a MIDI Baby 3, you could use one to control both SYN-2s, would need to set to different MIDI channels, and program secondary functions on the buttons to get all 8 channels. Some compromises in speed of channel changing over the GC or 2xR5s, but takes up far less room on board & costs less- depends on what you need.