As proposed in the main body of this piece, the addition of hou does not make achri more or less likely to restrict its temporal meaning to one interpretation. The following compilation is only a sample of the verses which testify to this fact.
No Cessation from the Main Clause / Hou Present
"For He must reign until [achri hou] He has put all His enemies under His feet." (1 Corinthians 15:25).
"But as the time of the promise was approaching which God had assured to Abraham, the people increased and multiplied in Egypt, until [achri hou] there arose another king over Egypt who knew nothing about Joseph." (Acts 7:17-18)
"Nevertheless what you have, hold fast until [achri hou] I come." (Revelation 2:25).
No Cessation from the Main Clause / Hou Absent
"I thank my God in all my remembrance of you, always offering prayer with joy in my every prayer for you all, in view of your participation in the gospel from the first day until [achri] now." (Philippians 1:3-5)
"Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned for until [achri] the Law sin was in the world " (Romans 5:13).
"Brethren, I may confidently say to you regarding the patriarch David that he both died and was buried, and his tomb is with us to this day." (Acts 2:29)
Cessation from the Main Clause / Hou Absent
"Now I say, as long as the heir is a child, he does not differ at all from a slave although he is owner of everything, but he is under guardians and managers until [achri] the date set by the father." (Galatians 4:1-2)
" and he threw him into the abyss, and shut it and sealed it over him, so that he would not deceive the nations any longer, until [achri] the thousand years were completed; after these things he must be released for a short time." (Revelation 20:3)
" they were eating, they were drinking, they were marrying, they were being given in marriage, until [achri] the day that Noah entered the ark, and the flood came and destroyed them all." (Luke 17:27)
Cessation from the Main Clause / Hou (hos) Present
"My children, with whom I am again in labor until [achri hou] Christ is formed in you but I could wish to be present with you now and to change my tone, for I am perplexed about you." (Galatians 4:19-20)
"And I saw another angel ascending from the rising of the sun, having the seal of the living God; and he cried out with a loud voice to the four angels to whom it was granted to harm the earth and the sea, saying, Do not harm the earth or the sea or the trees until [achri hos] we have sealed the bond-servants of our God on their foreheads." (Revelations 7:2-3)
"For I do not want you, brethren, to be uninformed of this mystery so that you will not be wise in your own estimation that a partial hardening has happened to Israel until [achri hos] the fullness of the Gentiles has come in; and so all Israel will be saved "(Romans 11:25-26)