I would not recommend the strap wrench.
This is the wrench I bought to carry on my S&S bike when I am not on a bike tour, this is what I carry when riding near home. I had to use a file to make the imprecise punch press manufacture of the wrench fit the S&S couplings better, but it is light and adequate. I bought this solely to get me home if a coupler loosened up on a ride, I envisioned no other real purpose although it can also function as a pedal wrench.
This is the wrench that came with my bike frame that I carry on bike tours, this is what I use to disassemble and re-assemble the frame after flying international, etc. Pedal wrench (15mm) built in, and I can use it to adjust my eccentric bottom bracket to adjust chain tension. The wrench was designed to handle all unique purposes for that specific frame.
Not really sure why they put an 8mm box wrench in that S&S wrench, but I cut a stub of an 8mm allen wrench that I can put in that box wrench to remove my crank arm bolts (square taper). I have to remove the crank arms to pack the bike in the case, I bought a crank arm extractor (XLC brand) that uses the 15mm wrench, so that S&S wrench is one of two tools I need for crank arm removal.
And don't suggest that I consider self extractors for my crank arms, tried them and one of the two self extracted somewhere in the middle of Iceland. After that I decided to carry real tools instead.
I suspect that even if the coupler was not tightened adequately, with those inner tube rubber sleeves, the coupler should not be able to freely rotate, so it should not be able to loosen up significantly. I still check the couplers once or twice a year to make sure they are still tight, but I certainly do not check them for every ride.