Hello, I can't tell from the information supplied whether you've been running 12Pay since April, or if you've just started. (ie does 12Pay contain the employee's pay since April).
If you have been doing that then all you need to do is change the employee's tax code, and they will probably pay quite a lot more tax the first month that you do this. You can do this right away, in the current month, and then reprint payslips/reports etc. You shouldn't need to do anything special to make it work, this is a really common thing. Because it is a cumulative tax code the exact monthly timing of the change really doesn't matter at all, cumulative tax codes are automatically self-correcting.
You'll need to change the net amount that you're paying the employee each month to reflect the changed circumstances, and because the tax code has changed the net pay may well not stabilise for a couple of months. So probably best to stop the standing order, pay the correct net each month, and sort out the accumulated £2.30 errors at the same time.
Then, ongoing, I'd strongly recommend that you pay the employee the correct net as shown in the payroll each month, not an arbitrary close figure to that. If that means that you can't do it by standing order then so be it. It'll make things a lot easier in the end, particularly if you ever got inspected. The inspector would expect to see employee payments that tie up perfectly with payslips and P11 reports etc and won't be impressed when you couldn't show them that.
Let me know if you need further clarification.
EDIT: You can see how much you owe each month (yellow book) using the P32 report, which can be printed from the top-level employer form. This report also comes out automatically each month from the payroll as you advance to the next month.