I've just reread your original post Doubting Thomas. From what I can suss out, you have already been able to move the location of the main event to a neutral location. That's grand. You seem concerned with the fundraising side, as you said:
"If we approach outside bodies for money on the basis of our constitution (remember, the one that says we're non-denominational) and then have a Mass at the event I'm concerned that we could be accused of taking money under false pretences."
I understand the conflict in many Irish minds over this, but as I said above, the organization doesn't exclude Protestants from membership or participation, therefore it is being true to it's non-denominational constitution. Having a religious service, as one of several activities, wouldn't mean you were taking money under false pretences, or violating the letter or spirit of the constitution. It merely recognises and honors what you also rightly point out:
"...(is the) perfectly understandable historical and sociological reasons most of our members in this particular area of the world are members of the Roman Catholic church."
In other words, you are honoring the Catholic ethos of the majority membership. It takes much more than just being Catholic, and having a mass with the event, to intentionally exclude Protestants. In my experiences in Ireland, I have always found that the organization in question bending over backwards NOT to exclude the Protestants, not the other way round. However, it was also my experience in Ireland that most Protestants refused to participate in anything remotely associated with the Catholic community.
Now, if that is what you perceive as "the dilemma" ie, that the Protestants are refusing to participate as long as there is a mass, well...you've gotten excellent suggestions on ways to try and make them feel more comfortable with the Catholic ethos of the organization. I think that is what the organization should continue to try and do, rather than cleanse the organization of it's Catholic ethos. Include the list of Protestant church services, work with the current membership to offer an ecumenical, or inter-denominational mass for the long haul, where both Protestants and Catholics can receive communion, that sort of thing.
But I think you are seriously misunderstanding the term "non-denominational", and interpreting it to mean "non-religious, secular activities only" which is the way many a person raised Protestant or Irish Catholic in Ireland in 50s and 60s would like this particular organization to be too. But as I said, that isn't what this organization is, nor do I believe it should change it's ethos, merely to appease those who don't like Catholics, be they Protestant or raised as Catholics themselves. Both are attacking Irish secular organizations with a Catholic ethos nowadays, and I fear there is a negative trend to throw the Catholic baby out with the sectarian bathwater. That just doesn't seem right to me.
(BTW, I and others have chosen to ignore your remarks about clergy abuse for a good reason.)