One change you can make is too allow more than 2 days to sign your own arb eligible players ( players that will be free agents next season) to long term contracts. Instead of having the player tell you that they are signing for free agency next season you can allow the player to extend his contract during the regular season. Currently WIS answer to someone who is unavailable for 2 days is too punish that owner by forcing his players into free agency, something the player would not of done if the owner was available for those 2 days. If your concern is the owner will get a extra season by arbing the player, then afterwards signing him to 5 seasons, then only allow players who went to arb to extend their contract 4 season instead of 5. You can pretty much adjust to anything to accomplish the goal of making this aspect of the game less time consuming without making the game less involved. Making a game unnecessarily time restrictive is not skill its luck.
I was just gone for 6 days on a road trip and the 2 arb days happen in 1 of my worlds. about 6 weeks ago I had to go away for the weekend, when I left Friday night I was not able to sign my players, when I got back monday morning the period already past. Its happen to me 3 times in the last 4-6 months. To me the most important thing is my players, and I am willing to bet that is the case with most people.