So it becomes a constitutional monarchy with a “Governor General” serving as the representative of a monarch whose government forgot they even existed? This neglect ironically gives them the freedom to form whatever government they want. Autonomy via apathy.
This will be the status quo for a while, but the neglect probably wouldn't benefit Guiana as much as it might other territories, Guiana's population is so low and the territory so hostile that the neglect stalls development until the government sets out to conquer the
Enfer Vert once and for all.
I suppose Guiana-sans-Cayenne's capital is at modern Kourou or somewhere around it? Seems like its main population would be soldiers for now, at least until the US starts using exile of political prisoners as a means of settling the peripheries.
The de jure capital would likely be Kourou or Sinnamary which are the only two settlements that would exist at the time that are of any relevance.
But on a slightly dark note, the settling of prisoners in Guiana would be a brutal way to populate the territory, but it could be effective, and even tie into the development of National Corporatism ITTL. A wrong idea on race that was common during this time period IOTL was that each race was adapted to a certain climate, so as Nat. Corporatist ideas begin to become widespread, people who are arrested could be deported to prison colonies meant for the "wrong" climate for their race as a method of punishment. It's horrible and would need more development, but it would fit with my plans for the Roosevelt dictatorship.
And then he married the Empess of Brazil, and the house of Lafayette ruled in peace and justice forever
A personal union between Brazil and the American Empire in Guiana would be amazing. Such an entity would directly rule 1/5th of the American continent, and ITTL claim
over half of the entire continent.
Sadly, Brazil probably won't exist ITTL.
So I'm gonna make some predictions for what will happen in the Austrian Empire:
The Austrian Army kills/sends into exile the Monarch or the Emperor takes their side and they become a Revolutionary Empire/proto-Fascist state
They then turn around and crush the Hungarian Republic, the Republic then becomes a symbol for Hungarian nationalists
The Austrians levee en masse and proceed to drive away the invaders
The Austrian state dies a bunch of Napoleon type stuff, before eventually being defeated by a coalition
A new ideology based on whatever type of that Austria becomes is spread and emulated by other revolutionaries.
I won't say what you got right, except that Austria will be defeated in a coalition. The Austrian Revolution isn't meant to be a direct translation of OTL's French Revolution, but defeat by a coalition as France was will happen. One of the differences will force a coalition to batter the Revolution into submission, although practically every power will be fighting for a different reason.