Ok, time to do some analysis. I'm assuming that people trying to win this are going to want to get most of their Wings via Globetrotter badges, since those are by far the most lucrative; and I'm also going to assume that people will want to get more than one Globetrotter badge per flight. Since we're talking about Air Canada here, I'm limiting consideration to flights which have at least one Canadian city.
This means that non-Canadian cities which only participate in a single Globetrotter badge can be excluded from EYW-running consideration. This rules out MIA, FLL, MCO, TPA, RSW (Citrus only), PHL, EWR, ORD, DCA (East Coast only), IAH, LAS, SAN, PHX (Sun Belt only), SEA (Mileage Run only), MXP, MAD (Palace only), MEX, KIN, MBJ, BGI (Happy Hour only), DUB (Castle only), CPH (Canal only), SYD, NRT, HND, ICN (Pacific only), GRU, BOG, LIM, SCL, EZE (Dulce de Leche only), NCE, FCO, BCN, LIS, ATH (Rouge only), HKG, PEG, PVG (Emperor only), MUC, GVA, and ZRH (Biergarten only) destinations.
This now rules out the Palace, Happy Hour, Pacific, Dulce de Leche, Biergarten, Citrus, East Coast, Sun Belt, and Emperor badges since there aren't enough "potentially worthwhile" cities left to make it possible to get those badges. Doing that allows us to cross off BOS, SFO, BRU, FRA, the Mileage Run badge, and LAX.
There are now 9 badges left:
Cross Channel (LHR, CDG)
Maple Leaf Lounge (LHR, LGA)
Castle (LHR, MAN, EDI)
Canal (CDG, MAN, VCE)
Rouge (MAN, EDI, VCE)
Theatre (3 of YTZ, LGA, LHR, CDG)
Scenic Drive (YWG, YHZ, YQB)
Prairie (3 of YWG, YEG, YXE, YQR)
Trillium (3 of YTZ, YOW, YQT)
With the exception of YTZ being an option for the Theatre badge, we now have two completely separate contests: The international contest, with 6 badges and 6 cities (LHR, MAN, CDG, EDI, VCE, LGA), and the domestic contest, with 3 badges and 9 cities (YWG, YTZ, YHZ, YQB, YEG, YXE, YQR, YOW, YQT).
On the international side of things, the most efficient option I can see (in terms of badges per flight) involves making round trips to LHR, MAN, CDG, LGA, and one of EDI, VCE; this would yield 13 Globetrotter badges. Along with the Destination badges (8x international, 2x US) and the default 100 Wings for non-Destination cities, this yields 13 x 2000 + 8 x 750 + 2 x 400 + 10 x 100 = 33800 Wings for 4 transatlantic flights (2 on Rouge) and 1 transborder flight. If you want to avoid Rouge flights, the best you can do is to hit LHR, CDG, and LGA for 6 Globetrotter badges -- 16400 Wings for 2 transatlantic flights and 1 transborder flight. Rough guess: $200 and 1 hour of flying per 1000 Wings.
On the domestic side of things, the only overlap between badges is YWG which appears in Scenic Drive and Prairie. I don't see any way to efficiently hit two of {YWG, YHZ, YQB}, and hitting all three of {YOW, YQT, YTZ} looks similarly awkward given the schedules Air Canada operates. On the other hand, with the Prairie Badge, consisting of 3 of {YEG, YXE, YQR, YWG}, we have a winner: A single $263 YWG-YQR-YXE-YEG ticket will net you 2 Prairie Badges along with 6 Canada Destination Badges, for a total of 5200 Wings. It doesn't look like you can hit both YXE and YQR when flying in the opposite direction, but still -- for a one-day "wing run", this definitely looks like the best area to hang out.
Canadiancow, over to you.