the americas look good on a map, but at the time (circa 1700), they weren't much of a game changer. Hapsburg Austria got Italy and the Netherlands. France got Spain as a nominal ally, which alleviated a threat to one side. they took absolutely no advantage of it, and instead looked to keep Spain as minimal as possible. long term consequences were that when France needed Spain, the most, in 1760, Spain was useless.
So, anything seen as worthwhile was taken away from Spain. Britain didn't want it's own ally, Austria, to get more, and certainly didn't want the enemy France to get more. Everyone was happy to see Spain get knocked down to a minor power. and everyone was exhausted after a decade or so of war. hard to see things change much. but.....the idea is to change it.
Someone has to get the Americas. everything else was already taken away.
France, Austria, Britain are the contenders. No one wants any of the others to get the spoils, which is why Spain got to keep them, but someone else has to get them in this ATL. France is the nominal winner, so they're front runners for taking them. they have Canada and Louisiana. Getting the rest of the Americas might make them more willing to wheel and deal on the Ohio country. They have additional responsibilities now for maintaining a navy and an army. this is going to be too much to chew.
Austria as a colonial power. yeah, they're going to concentrate on the German lands and ignore the Americas. it's hard to see Austria doing what it takes to become a global power. that entails getting a Navy, which OTL, they ignored. I have a hard time picturing Austria finding a place, or inclination, to port a Navy capable of projecting power in the Atlantic/Pacific. They're bottled up in the Med.
the Brits. they're the only ones capable of making it work. but, this is before their time of world domination. Do they have what it takes to occupy and control all of the americas? It is fraught with danger, but this has the making of a Brit wank. they're likely to be occupied with colonies, and thus won't be quite as obstinate over Ohio. I see major butterflies with the 7 yr war whether France or Britain get the Americas.