You can also go to Tanda of the Week to read about and enjoy a special discount promotion for these songs! And ofcourse check out all the D'Arienzo tandas on TOTW.
So far your best options for getting some of these songs in good quality have been the very rare Club Tango Argentino releases or albums like De Pura Cepa (Spotify link) or El Esquinazo (Spotify link). In some cases the differences in quality are minor and it's up to you which versions you prefer, although many of the CTA versions have a lot more record noise than the TangoTunes versions. Although the TangoTunes versions have gone through more remastering don't be afraid since the songs are not over filtered and the orchestras sound better than ever.
Nevertheless, I would like to especially highlight one song in particular: "Trago amargo" from 1939 with Alberto Echague. Unfortunately the short sample available on TangoTunes is not in full quality (low bitrate) and it fails to give a true example of the quality of the digitalization (which is available both in MPEG-4 and FLAC), but you can hear the clearness of the sound and that there is no record noise besides slight hiss, making this probably the best version available and at least the best one I've heard. I had to dig into my recycle bin to recover my older versions of the song to compare the quality further. I had the versions by Keith Elshaw (totango.net), Club Tango Argentino (CTA306), "Tango Bravo" (album), and also the collection "Su obra completa-Vol 06 de 48(1939-1940)". The last three suffer greatly from loud record noise, which just gets worse in the end of the song especially on the CTA version, and the last two also have very poor quality in general. The Keith Elshaw version has less record noise but unfortunately the way it is remastered hurts my soul. The "Trago Amargo" available on Spotify (and iTunes) from the The History of Tango / El Rey del Compas / Recordings 1954 - 1955, Vol. 7 album (which oddly enough includes actually the 1939 version of the song) also has similar record noise to the CTA version.
I've made a printable PDF file of the complete D'Arienzo discography between 1935-1939 with links to the songs available on TangoTunes.com as well as links to www.tango.info where you can find more information about the songs. Below are the songs from 1935-1939 available on TangoTunes so far. Also more shellac digitalizations are available and you can check them here.