Dear David!
In my mind the regulation you´ re refering to is not that confusing. The last sentence says that there might be alternate means published in the relevant state AIP. It is always up to the operator to have operational control over what is required in the the different airspace concerned. The local national CAA in this case should have issued a NAT/HLA Restricted approval for this A/C with no HF com radio. For example you can fly to Iceland and further over the Atlantic, but of course via specific routes with only VHF.
Brgds, Johan

Dear David,
There is no problem to operate within NAT HLA space where there is VHF coverage.
Best regards,
Vanya Naumova

Dear David,

I ferried an aircraft some time ago & can confirm that it is possible provided you fly the VHF routings. One thing to keep in mind is that you will most certainly be altitude restricted (usually FL 280 and below if I remember correctly).
Kind regards,
Stanko

For this "unusual" cases (and not only for them) I would check the ICAO DOC 007 as well...but you specify that the requirement from the Air OPS (965) point of view are an issue. From my experience it is, as Stanko Ivan Misetic pointed out, mostly about the FL restrictions...bellow the FL280 within the VHF coverage should be no problem.