The only one I have direct experience with is the BomeBox running MIDI Translator Pro. I use it quite a bit with logic statements, global variables, etc. If some of the others can do it, I’m not sure (See also MIDI Solutions Event Processor, MIDI Hub, Retrokits RK-002 “smart” MIDI Cable, etc) I’m sure Technobear will probably pipe up with his experiences with MIDIHub. The only people I “know” who use the MIDI Solutions or Retrokits are on Elektronauts.
Basically with Bome MTPro any MIDI Event can be translated to a different MIDI Event or series of Events, including storing or reading variables. If you use a computer (and have no issue with one if/when you’re performing or doing what you do with your rig), you can also configure keyboard buttons to ‘do things’.
Note: Just so this bit of info is in your head, it’s my understanding that the MIDI Standard usually says a Sequencer Start needs to be followed by a Clock Event, but I’m assuming this point is moot since the Clock would be running already. If you went the other way (starting the alternative sequencer that isn’t Clock Master first wouldn’t be possible in my understanding). That bit of info might factor into your ‘can I do this thing I’m thinking’ process.
Plus like Squarp, Bome has amazing support & customer service.
Edit to add: If you’re not against sticking a computer in your data chain at least for testing, you can start off with MIDI Translator Pro before investing in the hardware. I think you can even try the Demo version first (just can’t Save anything I think) to see if it works for you.