You're making it way too complicated.been thinking about this...and I have some questions....
(1) How many watches do they expect us to wear, in order to keep track of every player that has been given a 10 min sin bin ? 22 ? 30 ? If anyone says there is unlikely to be more than 1 or 2, they've obviously never refereed on Hackney Marshes.
(2) Is anybody going to officiate the bin, while the angry people are squaring up to each other (and the supporters) on the side of the pitch ?
Record the card like any other, then write the time they should return to the field of play.
You know whether you've got someone due to return, so just check at each stoppage when you know it's close.
People will square up on the sidelines anyway if they're going to. You just don't put them near each other in the first place when you can avoid it - stick them in different boxes outside their bench.
People love to complain about how badly things are done in other sports and bemoan the changes made to football, but maybe if people paid more attention to what those others do, the changes in football would be a lot less strifeful. VAR is another clear contender in this area.