Only thing I could suggest is calling the club or RFK, but it sounds some people have had problems with getting help that way too...

How would you have done it?

The club said that any remaining tickets will then go on general sale from 9am on Wednesday so I'm wondering if, as a non-member, I should be able to buy the dozen tickets I need on Wednesday.

A ticketing website owned by the club linked to your membership. Fairly simple and I'd guess there are even championship level clubs who have this

There's no point asking on here although I doubt you'll get 12 tickets together

But there isn't one, as we all know, so that is not a simple answer.

Watergate has nothing on Ticketgate....."Just follow the money."
Where's a bit of Deep Throat when you need it?

ticketing software is readily available (some is even free), you can also use third party companies and given what was mentioned upthread about the liklihood of events for CC/playoffs etc surely it would make sense to invest in this not only to make it easier for fans but also financially.
I mean if we are using the SMCs ticketing system for league matches anyway and no doubt paying for that too then why should the club rely on that then have a fairly muddled/cumbersome way of doing things which involves fans having to queue outside the stadium for a ridiculously long period of time on top of which the timing of when you could call for tickets and where in the stadium was available being unclear added into which we had tickets being sold through the RFL to non members.

Go onto ticketing site. Are you a member, A: yes, enter ID, choose ticket location/type that are available. Pay for tickets.
Are you a member A: No, sorry tickets for non members are not available until XXXX date at XXXX time as this period is alloted to give members chance to purchase.

It really doesn't have to be complicated nor expensive and if we are already using the SMC/hulltigers ticket system could it not work out cheaper and with more flexibility for the future?

Simple enough to put one in place

I realise that the simple answer is a ticketing system which caters for home, away and neutral venues, it isn't rocket science.
But the SMC could insist that we have to use their very limited system.
They own the seating plan and they own the turnstile barcode readers on which the printed tickets depend.
They also dictate which turnstiles are open.

The SMC probably charges city a small fortune to use the ticketing system, because it makes not a jot of difference to the Allams, in fact if probably works in their favour, so we'll probably be quoted inflated charges for extra functionality.

edit: maybe I should have said that an effective online system would cater for most people, as not everyone would have access.