i.e. on what legal basis do they define "completing the course to the tutor's satisfaction?
Courses have no legal basis whatsoever. There is no legislation covering either them being offered, taken or satisfactorily completed. Everything about the process is at the discretion of the police.
I suppose if you paid for a course and the police claim you did not complete it satisfactorily you could make a claim for reimbursement if you could show you did actually complete the course properly. However, legally that would not prevent the police from prosecuting you.
I suppose if they did you would have to to argue that a subsequent prosecution was an "abuse of process". Even though courses are outside the law, the police have taken money from you (via the course provider whom you pay) with a pledge not to prosecute you provided the course is completed satisfactorily.
But that's only guess as it is outside my knowledge.
I'm going to be away for a couple of months (contractual obligation) which may run over time so I chose the latest date I could, that being just 2 days before the date by which I need to complete the course. I'm sure it was 6 months, I'll check, but it will definitely be over 7 months since the date of the offence.
You may find that if you fail to complete the course by the six month deadline (whether you've booked one or not) they may prosecute you. Many forces have a habit of leaving beginning court proceedings until a day or two before the deadline is up. You may return from your trip to find a "Single Justice Procedure Notice" on the doormat.
You have two choices: ring them up to find out or don't. If you do, it my stir them into action when they might not otherwise have done so. If you don't and they do propose to prosecute you, you will be faced with much larger bill and penalty points.