I dealt with this on a previous boat. A little different situation because I was winderizing, but the same in that I needed to replace the sea water circuit with something other than sea water.
I used the same type of strainer cap with a hose fitting, except it was before Groco offered them and I had to make it myself from a replacement bronze cap.
I also made a general purpose "service" bucket that has come in hand over and over again. It's just a 5 gal bucket, and I installed a fitting and shutoff valve through the side of the bucket as close to the bottom as possible. That allows water to be drawn from teh bottom of the bucket rahter than pulled up over the top. for flushing something like an HVAC pump that has no lift capability, it allows you to gravity feed it.
OK, with that aside, I needed to flush prop glycol through the system, not just water, but the approach is the same. I did as you and closed the thruhull and filled the bucket. Then start and run the engine which would drain the bucket down very fast. Stop when the bucket is empty, refill, and repeat.
That flushes with 100% of whatever you put in the bucket. Getting back to your original question, my engines were QSCs, not QSBs, so a bit larger. And I also needed to get glycol into the muffer, not just the engine. So I needed more juice than you need to just get fresh water into the engine and the injection ring. I needed 15 gal per engine, and I think a significant part of that was the mufflers. So I would think 5 gal would probably be plenty for you, and 10 gal would be certain beyond any doubt.
I would not operate with the thruhull open. That just defeats the whole purpose.
You could run the hose to keep filling the bucket while draining, but that makes for a very difficult one man job. If you fill the bucket, shut off the hose, go start and run the engine long enough to drain the bucket, then go fill up again, it's an easy one man job. I always did it myself on our boat.
I would also let the engine pull water from the bucket, and never connect the hose such that the raw water system is pressurized. Not only do you risk damage to teh impeller, but you can full the muffler (assuming a water muffler) more than expected and risk back flooding the engine. It's not a certain problem, but an opportunity to make mistakes, forget to turn off the water, or whatever.