If the "part-time" instructors have no other source of employment income, then I'm surprised that the Revenue are accepting it. Probably more like, haven't got round to reviewing it!!! The Revenue are in a bit of a mess at the moment and many circumstances are going unnoticed rather then being investigated.
The circumstance which you describe does not indicate to me self-employed; the fact that you find PAYE difficult to administer is not a valid argument; Employer's NIC is 12.8% of gross pay (as near as dammit) so that should help in your cash flow management. Pay would be just as easy to predict as paying your instructors on their invoice. Benefits? You give them? Audit is straightforward; you keep records! None of this is unpredictable. Honest. There is no reason why you can't run ad-hoc PAYE. There is nothing difficult, different or complicated about the financial aspects of an aviation business (apart from the fact that it's a good way to make a small fortune!!) and these circumstances apply to many different professions. This situation is not unique.
Professional independence as you describe is NOT one of the factors which the Revenue would take into account. As an ACA, I am governed by rules of my Institute which override what my employer tells me to do. Similarly, with the commercial pilot's licence I would imagine.
This is just my humble opinion and all I suggest is that those of you in that murky grey area, be careful. You could get done!!