Your post lists plenty of reasons why staying on part time would be great for you, all of which are perfectly valid and if I were an employer looking to convince you to stay on part time those would probably be some of the arguments I'd use to try and persuade you.
In this case however you're the one trying to persuade the employer to agree to the part time arrangement - and to do that you are going to need to come up with some arguments as to why it's beneficial to them to do so.
Since you're currently employed full time then presumably there is sufficient workload in that position to require a full time employee so you're going to need to come up with either a solution to that shortfall. Such as:
Rather than going part time you do compressed hours so you cover the full-time hours over fewer days (might work if your role doesn't operate in a particuarly ad-hoc fashion)
Working a reduced number of days over all but with flexibility - so that you can be present more of the time when their need for your services is high and when work is slower you are in less (this would suit a more ad-hoc work pattern and gives the employer the possible benefit that they are only really paying you when they need you). You could do this either as a part time employee or as a third party contractor. Offering this as a contractor would then offer an additional incentive to them as they would be saving on any employment costs.
If however they do need a full time person in the role then you'll have to come up with a way to justify the additional cost to the company of having you as a part timer and having a full time replacement for you.
This is going to be tricky, you've only been there 8 months so it will be difficult to argue that the company would be losing too much in-house knowledge by letting you walk out the door, and given you state that this is mainly a learning opportunity for you it's unlikely that you are bringing sufficient levels of experience to the role to warrant hiring a junior or entry-level employee at a much lower wage than yourself and retaining you as a part timer for the "tough stuff".
I've got to be honest and say that your chances are slim unless they have really been struggling to find enough work to fill your full time hours. Asking if you could stay part-time as a contractor is probably your best chance but I think you need to be prepared for the "No".
If you're happy with the idea of leaving if you don't get the part-time deal you'd like then there's no harm in asking though.