ALSO - in order to prevent the problem from happening again, I have the faucet just barely cracked open about 1/16 of a turn or less.
I'm thinking, maybe I had the faucets open too far and street pressure was overloading the floodsafe safety valve.
If the faucet on the wall is only open a little bit, when the solenoid opens, there won't be a huge rush of water through the connector hose that could trigger the FLOODSAFE connector's safety valve to shut off.
So when I reassembled everything, I shut off the hot and cold faucets, then set up the washer to fill with only cold water, and I started the timer running with the faucet still off.
Once the timer is running, the solenoid is open.
Then I very gradually opened the cold faucet a tiny bit, so the machine was filling but not quite as fast as it could have. Then when I had that faucet adjusted, I switched to hot fill, which opened the hot solenoid, and repeated.
Now the washer fills about as fast as it ever did, but this time the narrowest point in the system is at the faucet on the wall, not inside the FLOODSAFE valve in the connector hose, so I'm not teetering on the brink of the having the FLOODSAFE valve trip and shut off the water anymore.