Not a scholar, but I am a history nerd and a bona-fide successful completer of Con Law I and II at a relatively reputable American law school. In the absence of any responders meeting a stricter standard, I'll take a crack at it. The mods at /r/AskHistorians would slap me down in a second, however. :-)
I think it would be fair to say the founders, as a group, acknowledged a well-accepted fear of a standing army, but the degree to which individual founders were "vehemently" opposed and the degree to which they expected that fear to hold up if the Constitution enabled a stable republic would have varied. Hamilton was well known to have been in favor of a standing army and viewed Article I-8-12 not to have banned one, but rather a compromise in its requirement to re-authorize its funding every two years, barring a declaration of war. He viewed a Federal Army as potentially better managed than militias and was writing in response to anti-Federalists, acknowledging the general trend disfavoring them. Jefferson would have been one of the leading voices against standing armies, and even Madison came around to disfavoring standing armies, though he certainly had his hand in drafting the Constitution as it was ratified. With various degrees of trepidation, the "founding fathers" supported a constitution that they knew had certain allowances for standing armies, and lingering anxieties directly led to the Bill of Rights as a compromise to those concerned with the Constitution as written.
Calling up the militia would most likely have been considered the main means of constituting a fighting force, but I think there are at least some other hints that a standing army was not intended to be completely anathema. In the absence of the 14th amendment, the 3rd Amendment would almost necessarily have contemplated peacetime quartering of Federal troops.
Then you have what really happened. Washington was known to be a sort of soft Federalist, but it had no impact on the almost universal support to be the first president. There were already a few soldiers retained after the disbandment of the Continental Army (and indeed, it's disbandment was explicitly noted as being necessary for liberty), but in his first term the Congress immediately authorized a small standing army, and in the Adams administration a few years later, a huge army was contemplated, if never actually mustered.
So, in the end, it's probably in between, but maybe leaning just a bit more towards your interpretation. The idea of a huge, power-projecting standing army is really more of a post-WW2 thing, but one of the reasons it happened is that there has almost always been something, and the fundamental right of the government to establish one has been there from the beginning, though it was a bone of contention in the early debates around the Constitution.