I am no expert but here's what I believe you must do:
1) You do need a valid Canadian license; therefore, you do need a
CANADIAN medical. How to get that in the US I don't know.
2) I believe that your Canadian Pilot Licence is *VALID* as soon as you
get your Canadian medical; therefore, you can then proceed and get your
US currency (which I believe is fulfilled by the BFR).

I do not believe that you have to be *CURRENT* with your Canadian
license. However, below are the Canadian currency requirements.

Good luck,
Gerd (ATPL, Canadian)




FIVE-YEAR REQUIREMENT
CARS 401.05 (1) No holders of a Canadian flight crew permit, licence or
rating shall exercise the privileges of the permit, licence or rating
unless:
(a) the holder has acted as pilot-in-command or co-pilot of an aircraft
within the five years preceding the flight; or
(b) within the 12 months preceding the flight
(i) the holder has completed a flight review, in accordance with the
personnel licensing standards, conducted by the holder of a flight
instructor rating for the same category of aircraft;
(ii) the flight instructor who conducted the flight review has
certified in the holder's personal log that the holder meets the
skill requirements for issuance of the permit or licence set out in the
personnel licensing standards; and
(iii) the holder has successfully completed the appropriate examination
specified in the personnel licensing standards. (Refer to "Recurrent
Training" below.)

TWO-YEAR REQUIREMENT
(2) No holder of a flight crew permit or licence, other than the holder
of a flight engineer licence, shall exercise the privileges of the
permit or licence in an aircraft unless the holder has;
(a) has successfully completed a recurrent training program in
accordance with the personnel licensing standards (see "Recurrent
Training" below) within the 24 months preceding the flight.
(b) in the case of an aircraft other than a glider or a balloon, where
a passenger other than a flight test examiner designated by the
Minister is carried on board the aircraft, has completed five night or
day takeoffs and five night or day landings, if the flight is conducted
wholly by day, or five night takeoffs and five night landings, if the
flight is conducted wholly or partly by night.
(c) in the case of a glider, at least five take-offs and five landings
in a glider, or two takeoffs and two landings in a glider with the
holder of a flight instructor rating - glider and obtained a
certification of competence to carry passengers on board a glider from
that holder in accordance with the personnel licensing standards.

SIX-MONTH REQUIREMENT
You cannot carry a passenger unless within the six months prior to the
flight you have completed at least five takeoffs and landings in the
same category and class of aircraft, by day or night if the flight is
to be by day, and by night if the flight is to be by night.
Category means aeroplane, helicopter, etc., and class means single or
multi-engine, land or sea.