-Library - Straight downgrade. There'd be less unused space so we can't get the best possible locations(we ideally want somewhere high on a peak, better for books if the climate is naturally cool, and less likely for gribblies to burrow in), there'd be less turns putting out the word to the caravans, less time for the scribes to get copying to feed the hungry, hungry maw of the library. Money doesn't improve it at all, the bottleneck is transport and production.
-Research institute - Ambivalent. We DO lose effective AP the longer it takes to set up, but at the same time its also easier for a richer and proven stable Eight Peaks to attract skilled academics willing to move out into the boonies, because there'd be an economy capable of meeting their luxuries wants.
-Sanctuary/Branch College - Same with the research institute, but less urgently so. No spellcaster persecution on such a scale, and it'd probably be easier to justify a bit later on to our Imperial superiors(the Colleges will understand but political fiction wise we'd really want either Lord Magister or Great Deed to paper it over so the fearful ones don't freak)
-Dreadnought - Well its definitely improved by waiting. I don't see why I'd want it, but if you want a dreadnought you want to wait. Preferably dig another canal so you can sail it right up to Eight Peaks why no?
-Karag Mathilde - ...
Library: Worse comes to worse, perhaps we might have to build our Library near the snowline of Karak Ziflin, on the border between the Dragon and the rest of Ziflin. I doubt
anybody is in a hurry to claim that area and it fulfills the requirements you've identified to locate the Library. But would anybody visit at the literal foot of an Emperor Hysh Dragon? How would a Hysh Dragon react to a giant repository of knowledge being parked beneath his house?
Research Institute: It sucks to lose those effective AP, but delays probably make this institution easier to build for many, many reasons. Then again, if the Satellite Campus of the Nuln Engineer's Guild takes off in the Eight Peaks, that probably represents a successful test-case that makes for a strong case of the viability of an Academic Research Institute at the Eight Peaks to prospective Academics and scribes, publishers, secretaries, research assistants and so on
open to all races who are not current enemies of the Dawi.
Also, it isn't just Ivory Tower Academics we want, but also Explorers and Adventurers as
@Alratan puts forth. I do think that if it becomes clear Mathilde's Research Interest such as the Waystones will be
very well served by mounting expeditions (which are AP sinks), just the prospect of the Research Institute reducing the number of AP,or even rendering preparing for expeditions outright AP Free will probably make advocating for a Research Institute/Royal Society all the more persuasive.
Sanctuary: I can see the thread being more comfortable with a "branch", in the sense of a Wizard base (not a teaching institute) in the Eight Peaks if we can lay our hands on a Second Great Deed, or already made Lord Magister with or without the Great Deed.
Dreadnought: Can a Dreadnought sail up to Ulrikadin right now, I wonder? If Mathilde was to switch to adventuring to the wider world from her home in the Eight Peaks, I foresee Ulrikadin being our key port of departure.