Possible solution:
Apply for Citibank card (CB)
Include 'balance transfer' application in card application - close the other two cards, and CB gives you 2 points per $ transferred over to CB.
Join QFF - cost will be $82.50 but worth it over the years.
Transfer all your points from AMEX and the Visa to QFF (those points then become QFF points, and won't expire as long as there is one action on your statement every three years (it might be five).
Despite what CB says (about closing your other cards for you).... you actually have to do it yourself (once the transferred funds have paid out your balance).
Once paid out, tell AMEX / Visa you had to close the card /s in order to apply for a mortgage loan... ask for a refund on the unused portion of the annular card fee. They may refund, or they may not.
That's about it....
good luck,