I don't think that the ex-CMB fares are subject to HIP checks- unless that's changed recently.

OP- perhaps try booking using 'Must fly on these dates' (instead of flexible dates)- I used to get the lower 'I' class fares instead of 'C' that way, for ex-CMB bookings, assuming of course that I class is available on the dates/flights you are looking for. An alternative is to email the CMB reservations team & book.