Interesting photo,
Relatively new construct (i.e. Arc Fault breakers for the bedrooms) and 100% populated. Your electrician didn't do you any favors (although it is a neat install).
Certain load boxes support the use of tandem 1/2 height breakers. This might allow you to replace two of your current 1" breakers with 4 1/2" breakers. You'll need to look at the load cell panel to determine if your box supports this. Don't install them unless it specifically lists the 1/2" breakers as supporter - code violation again.
An example of a tandem 1/2 height breaker is located here:
15A Tandem breakerThis can get you around the lack of open breakers, but you will still need to run a circuit outside the panel to mount your repeater (i.e. drywall saw).
A less invasive option might be to parallel an outlet box off one of your 220V terminations. It appears you have 3 220V devices (one 30A). If the 30A breaker is for a well pump (??) you could parallel off of the switch with your "coupler box". Not optimal due to the distance back to the main panel, but it may be easier than cutting out drywall and I don't believe it violates code.
Boiler