(I've no academic authority to write on the history of tango music: I'm just trying to work it out for myself. What I've written may well be wrong in places, but it is based on the stories in Todotango and Wikepedia. & it's based on my own ears, what I've heard when I've listened to the music, so of course it is partial and biased: no apologies for that.)
I get the impression that at the end of the 1920s and into the 30s Carabelli's recordings set the pace, arrangements written by a highly skilled classical musician experienced in ensemble playing, who was excited by the rhythmic vitality of jazz and was also respectful of the tango of the day. Busoni thought of music without prescriptive labels, and Carabelli chose to make tango richer, he took tango to a new level. To me his recordings are the earliest tango that actually sounds like the tango of the Golden Age. I can't help hearing, for instance, a direct link between the music of Carabelli and Pedro Laurenz. Not only did Laurenz play in the OTV, but his tango sounds rooted in Carabelli as if Laurenz, with his powerful sense of rhythm and energetic playing, turned up Carabelli's more restrained music to 11.
There are other links between tango and jazz. Fresedo had visited the US as early as 1921, but I've not noticed much jazz influence that early: it seems it was Carabelli who made decisive use of what he'd heard in jazz. Fresedo, of course, recorded some marvellous tracks with Dizzy Gillespie much later in 1956.
I've just come across this, tango in 1912, when Canaro was 24, when Carabelli was still in Bologna. But tango recording started to peak in the late 20s, when sound quality was reasonably good. Records must have made a huge difference. For the first time musicians could listen to a wide range of music whenever they wanted, and could listen over and over again and explore the details, finding out how and why a piece sounded as it did, instead of relying on piano scores, the bare bones of a piece, or a transitory live performances, or half-remembered renditions. I'm sure the availability of recordings must have contributed to the speed of change in the music.
& I'm curious: I'd love to know what was in Canaro's record collection in 1930, or Fresedo's, or D'Arienzo's! For sure they'd have had a Victrola at home, at least so they could listen to their own recordings, and shelves of 78s. I wonder if we'll know some day: I assume that the history of the music and the dance are subjects for research in Buenos Aires. Perhaps one day there will be a really detailed history, hopefully in English. I enjoy Canaro a lot, but on reflection it occurs to me that the Canaro I love has always been between 1929 and the late thirties, a period during which his music became more supple, it 'sang', he didn't want all the notes to be the same length. Earlier Canaro is a bit rigid, and his later music is often quite strident.
It's not so easy to find the recordings Carabelli made under his own name. I've got the Buenos Aires Tango Club (BATC) CD, which is excellent: buy it and you support local enterprise, and the activity of people who really care about preserving their music. They issue two other CDs: 'Inspiracion' with many of the same tracks as the BATC CD, and 'Mi Evocacion', which is the CD on Spotify, and is a mixture of dance music, some tango. Check out their catalogue, which is huge and excellent. They don't sell downloads so it means importing CDs, but their CDs are probably cheaper per track than buying downloads.
iTunes has three CDs, but I haven't downloaded them, so I don't know what's on them: they may also be a mixture of different kinds of dance music. El Bandoneon in Barcelona has a CD, but it is out of stock. Amazon UK currently has 71 tracks for download though some tracks are duplicates and not all are tango. But at least La Guiñada, and Quatro Palabaras are there. (If you don't mind contributing to Amazon's untaxed profits, that is.)
As to OTV, there's no shortage of recordings of this marvelous music. Spotify has a number of albums, and the two-volume Euro Records selection is available from BATC. (Euro records is part of the BATC: same catalogue.)
Perhaps it shouldn't be surprising that it is all so good: I've yet to come across anything from Carabelli, whether as Carabelli or as OTV, that wasn't really excellent. His name deserves to be known better. It's not that he's undervalued: his name just isn't known, but I believe he established the tango we still dance to.
PS: Simba Tango drew my attention to the Tangohub summary of places to buy tango, particularly from a UK perspective. There are warnings there about BATC, about the time it can take to get CDs from them, and also about the quality of the CD discs they use. However, there's a wealth of music in their catalogue, and the prices are good. If you have a friend visiting BsAs, their office/shop is just off Corrientes a few blocks from El Beso: otherwise, if you want to make a serious order I'd think of calling and talking through the delivery options with them (or get a Spanish speaker to call for you) before ordering. As to quality of the actual discs, it's normal to rip them to lossless anyway.