The overdub hack in Enso kinda works, but then if you go half or quater speed - the click is sometimes there, in one (or the other) channel. Its not super obnoxious, tho, so I might rule this off as an intentional artistic choice 
UPD: Basically Tiger-Lily is what exactly what I knew I wanted, and RE-1 is something I didn’t knew I wanted until I’ve tried it) You can ever interrupt the tape there)))
Thank you dearly everyone!