The AJA Gen10 is capable of outputting both “normal” and Tri-Level sync. You might consider using its dual outputs and sending each to a DA for distribution to your various pieces of equipment. Do you have equipment that actually requires Tri-level sync? If so, it should be happy with the Gen10 signals. I’m running one in a remote truck and it works well.
Unless you have a number of “islands” of equipment, you are generally better off running the same reference to everything. You can’t go wrong with everything locked to a common reference.
If you need something other than simple Black Burst, you might want to consider a more capable sync generator that is capable of a wider variety of output signals, although there isn’t as much of a demand for signals like horizontal drive, vertical drive or blanking as there used to be.
Not my monkeys. Not my circus.