A fair point. But it's much easier to maintain such a system in a world where people hadn't considered independence, than to try to start a union. Spain was also a superpower when the USA at this time was not. Let's remember, Jefferson always thought that if white English settlers reached the far coast of North America there would be a separate "Republic of the Pacific", so I can't see a fledgling US doing it to South America.
Jefferson was far from being the beginning and the end as far as the Founding Fathers were concerned, and if anything, ITTL his ideas on how to run the young republic get discredited more than OTL. And remember, his prediction ultimately turned wrong.
I can easily admit that a very important factor for bringing Peru in the USA so early was the British colonial expansion in Rio de la Plata. It's quite plausible a UK reaction to total loss of British North America, however may or may not happen in similar TLs. Without it, it is possible that a USA that follows a similar evolutionary path to USAO only ends up assimilating Canada, Mexico, the Greater Antilles, Central America, and Gran Colombia before the Gilded Era. But there is no special good reason why it ought to get anything less than that.
OTOH, after the Civil War, Pan-American expansionism is wholly bolted to the collective consciousness of the nation, the latter demonstrably treats its Hispanic citizens very well, so it is quite likely that Peru-Bolivia and Chile-Argentina, just like Brazil in the current near-future of the TL, would have been annexed, either peacefully, or through a few "wars of liberation".
I can understand the alliance between the founding fathers and libertadores. In the same way, there was a very fond relationship IOTL between France and the US, but union was never proposed after the French Revolution. A close friendship and alliance is as good as could be got I think.
It seems you undervalue the impact of the Pan-American ideal, if allowed to thrive in near-optimal conditons.
I really struggle with the idea of the US, or indeed any white country at this time, being as multicultural as they would need to be for this to happen. Quebec is one thing, but they're white Europeans next door. You would also need the multicultural mindset on the Spanish side too...
This is why it is so important that the newborn USA develop an assimilationist attitude towards North American "civilized" natives during the formative event of their culture, the ARW, by the Iroquois Confederation siding with the Patriots. Once this is ingrained, to accept natives and mixed-bloods of Spanish colonies, which were even more "civilized" to begin with, becomes a natural extension. Likewise, the presence of Quebec in the ARW ensures that acceptance of Catholic Romance-speakers gets bolted to the idea of Americaness. From French-speakers to Spanish-speakers, the leap is quite narrow.
As it concerns the Spanish side, this is where US intervention in the Spanish American wars of liberation is so important: it establishes a pro-US mindset in the formative event of Spanish American culture and its early leadership. With war-forged brotherhood and growing economic and political ties, acceptance of Pan-American unity becomes a natural development.