I don't think this is doable for a couple of reasons:

1. Departures to Canada are done in a US zone--meaning you have to be in the US. Most US airports don't have transit areas (like YVR, LHR, etc.). So, you'll have to clear customs and immigration for the US even though your only passing through.

2. Horizon flights (Alaska's short-haul partner) don't regularly post gate information and they're not consistent. This means that you could potentially leave out of the S-Satellite, the C-Concourse, or the N-Satellite. You probably won't leave out of the S because they usually use that for international flights. But flights to major Canadian cities (of which YEG is one) don't follow this rule. That's because there's a US customs facility in Canadian airports. That's a shame because you'll actually fly BA into the S-Satellite. So, most transiting passengers must return to the main terminal clear security again (there's also security inbound after immigration) to get to the connecting gate. Returning to the main terminal will involve taking an airport train--efficient yes, but time you may have to cool your heels. If you depart out of the N-Satellite you actually take a different train.

3. Baggage is relatively easy to deal with. From LHR you can have the agent tag your luggage all the way through to your destination, even though it may span multiple carriers. The catch here is that you have to "enter" the US and then clear customs--which means fetching your bags anyway. You re-check your bags for your desination (YEG) once you leave the customs hall. BTW, you must do this again in YEG (without the recheck part).

Within 1/2 hour? I doubt it--particularly since the immigration lines have been known to be long (sometimes 30 minutes or more). Your best bet (at least stressful) is to wait for the 19:50 from SEA to YEG.

Not to question your travel motivies (nor turn you away from SEA), but BA has a n/s to YVR--in which case you would have avoided the double-immigration/customs issue.