That's a good idea, I think. What Argentina needed urgently at this point was not so much investment (which of course wouldn't have been turned down, it just wasn't the primary need) insomuch as an export market. Exports to the British had made up the majority of Argentina's trade, and them turning to the Imperial Preference System royally fucked us over. Germany has very much the opposite problem: their lack of an empire deprives them of both markets for their goods and the availability of resources. That means that a free trade agreement would be very much natural, even if investment is not in the cards yet.
The problem I can see is timing, however. The treaty you mention, the Roca-Runciman Treaty, was signed in May 1933, and we are already past that ITTL. I guess that a willing Germany could still change the game, but from a legal point of view I'm not sure how binding the treaty was.
As you mentioned, timing is a problem, and even positive trade relations wouldn't have wedged Argentina out of Britain's sphere fast enough to prevent that. What I'm looking towards instead now is the possibility of Argentina peeling themselves off of Britain, either with active German aid or not, by taking advantage of certain geopolitical shifts in the late 30's and early 40's which will keep Britain distracted and Germany more at the forefront.
Brazil could look for it, Vargas was very much a opportunist and third wayism type of fellow and while this isn't exactly Hitler's Germany, he would very much love the ideal of having someone LB helping him modernize the country, especially given Vargas persecution of communists as well as the massive German population in southern Brazil who wouldn't be discriminated like otl and would support approachment with "the mother country "
The Italian population in Brazil is much larger than the German population.
The issue is that Brazil is a Latin-speaking, Catholic, modern Authoritarian nation, while Germany is pushing towards something which, on paper, is old-fashioned, at least in governance. I feel that Italy would be a more natural friend, especially since many of Italy's friends are also not conventionally fascist.
Another hot-button region I see is Venezuela, which is run by a military dictatorship, has enormous oil reserves, and which claims territory from its neighbours, notably the Dutch in the ABC Islands and British Guyana.
Aside from those, my knowledge of critical junctures and the influence of WW2 and its lead-ups IRL in the region is sadly lacking. The only other major factor I know in the region is the United Fruit Company, which, while undoubtedly affected by changes in the global market brought about by war, also wouldn't be massively different without some major divergences.