hmm.. ottos grinding to a halt camer earlier. 1684 it was painfully obvious they had outdated armies. Not to forget Lepanto in 1571 either, that was the destruction of their naval supremacy, but at land they could still field enormous armies, mostly due to overpopulation and urbansation in the levant.
But the tech started lagging soon enough, mostly due to the power of said janissaries that wanted to see no change... perhaps a bit like a similar issue in middle 19th c nippon?
In the ottoman empire however they couldnt solve the those problems until 1820 when all the janissaries were slaughtered.
And even then, the empire lacked the ability to reform itself. It fell much upon germans, britts and french to do that. Did you know that napoleon was to go and reform ottos? Well, then the revolution happened and he never got to go to constantinopel.... sure would have been a sight, a reformed ottoman empire along napoleonic lines OT: Althought to be honest, much groundwork was done by the brutality of robespierre. But still, lets not underestimate the administrative genius of nappy.. repayed debt, built, and waged wars all at the same time! A bit like as if bush today would instead of producing decifits be building a few more hooverdams and also repay all old loans and even save up a few hundred billion extra..
Ahem. Sorry about the rambling.
Anyway.
The main problem with a colonising ottoman empire is the internal organisation of said empire. The empire had only very little taxright, for example no incometax or such were ever levied, only import and export tolls.
Also the sultan had no ownership of any land, all that was directly owned by the subjects. All of this led to massive underfunding, or to be more exact, lack of funds. Inability to reform due to thgis lacking of financial power.
This naturally extends to the new world, how are the empire to fund an expedition.. and why? Afterall, its only those that come later that will gain the benefits, and with little cost of their own, so a project like that would have a massive negative net present value. And this wouldnt improve over time, as all thats aquired becomes the ownership of the individual.
So whoever is the first, loses, and those that come next wins. So noone will ever be first, and the state lacks the funds.
The great benefit is here a possible cure to what later plagued the empire: Unemployment. Population rose fast in already cramped lands, and little new opportunity. This all created further poverty asnd misery, all of which leads to instability and even more poverty and unemployment. Something much familliar to those looking at africa in the 1960:s and later im sure.