I see no problem with your terms, if only you will compromise to a few concessions. For starters, whereas I strongly support the faith's involvement in the populace's education, You have agree that the current degree of intellectual acumen for the vast majority of the individuals under Nova rule is deplorable at best; if given control over the realm's educational facilities, it is only fair that you be held accountable for improving said ratings, even if it takes Nova funding. Likewise, I shall not stand for Reformed bias: should they choose to adopt the Reform later in their lives, that will be their choice, but, the children are not to be taught such precepts within state-sponsored facilities.
While it is only fair that you, as the Si'kar Archon, be given ultimate authority over the realm's religious matters, including the condition of its religious infrastructure, I will veto Nova the right to fund improvements on said infrastructure in the name of the faith. However, you will be given control over both the priesthood and the tithes which would usually head straight for the Church proper. You will also be granted access to the research team, as requested, although I expected at least part of whatever is uncovered to be imparted to the House at a later date.
Remember that, unlike my fellow nobles, I fully support said "Black Robes" in their many endeavors, rescuing Aeverys without proving her innocence first is borderline blasphemous. In a similar light, whereas you are right in that the diocese depends on the tithes provided by the realm's faithful, you are, in all but name, a noble, in that you are currently holding a rather significant amount of land, Your Eminence. How may Nova's reunification efforts be ever successful if no less than 30% of the planet is held by spiritual authorities, in lieu of the planet's temporal authority? Know that, barring orders from the Orthodoxy stating otherwise, I eventually expect the land to which Nova, as the planet's foremost noble family and proprietor during the Imperial era, is entitled to be returned, just as you are you to be given control over the realm's spiritual matters.