Avid used to sell MediaStation just for that purpose, I don’t think that exists anymore. However, I think MC can be controlled over 9-pin as if it were a VTR (you will probably need a VTR control cable for that at least, which is different from the control cable you use for capturing), so maybe, just maybe, you would just be able to hook up the Avid as a deck, and then there would be no difference between TK to tape or straight into Avid.
Also, I did a film last year where there were digital dailies. The lab (Deluxe NY) had a virtual VTR capturing from the TK. They made DVD’s for the producers and DNxHD MXF files for the editing from that.
There’s also the Aja Ki Pro that you should be able to use as a RS422-controllable ProRes deck (haven’t done that myself, just saying it might be an option). You would then access the ProRes files through AMA, and transcode into DNxHD very quickly.
Either way, you’d need to do some serious back-ups, as you wouldn’t want to go back into TK hours once you lose a file.