Another possibility would be to somehow (see below) know when ARB transactions are submitted and to, if there is enough of a time window be capturing the transaction and batch settlement, to void the 12th one. If the time window is too small or unreliable, then immediately credit the transaction for the full amount.
As for how to know when ARB transactions are submitted, you could either go with SilentPost or use the ARB email notifications.
- SilentPost - With SilentPost, you configure your account to make an HTTP POST (aka form submit) to a URL you specify whenever any transaction (ARB or not) is submitted to your account. The form fields of this post are the fields of the transaction. This is fairly easy to implement, but the downside is that the Authorize.Net servers do a fire-and-forget when making the HTTP POST call, so if there is any breakdown in communication between their server sending it and your server receiving it, the notification is permanently lost. The reliablity of this is somewhat dependent upon reliable your website and hosting provider are, but overall the chances of there being a problem during those few seconds of the year when you need the information being posted (basically, the time a post takes times the number of customers on this 11+1 plan of yours) is probably quite low.
- ARB Email Notifications - In this method, you configure Authorize.Net to send you one or more emails on every day that at least one ARB transaction processes. Unlike the SilentPost method, emails are queued in an inbox, so messages are not lost because your website or server was offline the moment the message arrived. The downside here is the cost of building this infrastructure. You need to build a program, completely separate from your website, that runs on a periodic basis ("cron job" in *nix world, "Scheduled Task" in Windows) and checks a specified email inbox for messages matching a certain pattern (probably based on the sender and Subject line of the ARB notification emails), then download any such messages, extract the attached .CSV files, parse said .CSV files, and act upon the parsed contents accordingly. More reliable, more cost.
- GetTransactions - A third possibility occured to me while I was writing the above two. There is a fairly recent addition to the Authorize.Net API which allows you to download transactions. You could build a program (again, separate from your website and scheduled to run daily or as often as you need) that downloads all of the transactions for the last 24 hours (if running daily, otherwise since the last time the program ran) and looks for ones that need to be voided or credited.
I don't know to what extent you were hoping for a solution that did not involve programming, but I don't think there is one. However, if you can do it, any one of these three should fit the bill.
