You are absolutely right that Jer. 31:31-34 and the verses in Mat. & Mark do not refer to the same period. The only way that Jer. 31:31-34 makes sense is to understand there will be a Millennial Kingdom on earth after the Tribulation.
You summed up Walvoord's article beautifully.
As Walvoord wrote:
The amillennial argument breaks down, however, not on the basis of these finer distinctions but the obvious failure in the present age of any literal fulfillment of the covenant with Israel. As in other particulars of prophecy concerning the millennium, a literal fulfillment demands a future millennial dispensation.
The writer repeatedly exhorts Hebrew Christians to hold fast to Christ: "For we are made partakers of Christ, if we hold the beginning of our confidence stedfast unto the end," 3:14, for instance; and not to fall away, for if they do "they crucify unto themselves the Son of God afresh, and put him to an open shame," 6:6.
Hebrews addresses an ongoing crisis of faith taking place, Hebrews, therefore, addresses the here and now when it gets to the subject of the new covenant. What is to take place beyond the 2nd coming is not the subject.
To read a dispensationalist new covenant into these particular chapters in Hebrews, is to read something into the text that isn't there.
I say these things as a Historic Premill, by the way, I am neither Amillennialist nor Dispensationalist Premill.