I don't like IRV because I've observed that it has the same plurality issues that FPTP does. It's used in Australia and France, which both have quasi two-party systems: in France it's PS or les Républicains, and in Australia it's Labor or Liberal.
In my opinion, MMP best near winner is the best compromise:
Sainte-Lague has messy party lists. Party lists in general are a pain. Closed lists can lead to party interference with candidate selection. Open lists, present the risk (however small) of the rise of fringe/kooky candidates, like in the Netherlands and Scandanavia (Geert Wilders' PVV; FrP in Norway, SD in Sweden, PS in Finland and DPP in Denmark). I don't want to see a "Soldiers of Mackenzie" street patrol pop up in Canada, harassing newly-arrived Syrian refugees under the guise of protecting "old-stock" Canadians. MMP BNW has no lists at all, solving that issue.
Non-BNW MMP: New Zealand and Germany both have an MMP system based on constituency seats (distributed via FPTP) and PR seats (distributed via Sainte-Lague). In both these countries,s maller parties tend to only get seats in big cities. In the Bundestag's 2013 election, for instance, Alliance 90/The Greens got most of their support from the biggest cities in Germany: Berlin, Frankfurt, Munich, Koln, Stuttgart, Hamburg, Gottingen, etc. Therefore, their PR seats were clustered around urban areas. There is a self-correction mechanism for this in BNW (at least how it's done in the German state of Baden-Wurttemberg for local elections), wherein the state is carved up into four larger sub-regions (based on geography and not population), and the "near-winner" seats are distributed among those 4 sub-regions. This way you're not getting smaller parties clustered around cities.
D'Hondt Method stamps out smaller political parties (and also uses party lists). Why should one party with 40% of the vote have more seats than two parties with 20% of the vote each?
Largest remainders can lead to an apportionment paradox, better known as an Alabama paradox. After the 1880 census, the Census Bureau found that Alabama would have 8 congressmen if the House of Representatives had 299 members, but 7 if it had 300. While the size of the U.S. House of Representatives has been capped at 435 members since 1929, there is no limit to the number of MPs that can sit in Canada's House of Commons (Between 1988 and 2016, the House grew from 295 to 301 to 308 to 338 seats), so it is still susceptible to an apportionment paradox.
STV-P3 has a few problems.
Logistically, it could be a mess. This is because the LPC has a mandate to implement electoral reform before 2019 (by the way, I hope the Liberals eventually get rid of the very undemocratic concept of fixed election dates), which gives the government three years and change to redraw boundaries and implement the system.
An STV system is also harder to understand, moreso with P3, (even I can't make heads or tails of it, and I'm acquainted with other systems like D'Hondt and least averages), which will be a pain for Elections Canada and also make voter education more difficult.
It's likely there will be over-representation in rural areas or Canada's north. This could be solved by varying the number of seats in an STV riding by region. The City of Vancouver might have STV ridings with 5 members, and suburbs like Burnaby or New Westminster could have STV ridings with 3 members, and rural areas like the Peace Country could have STV ridings with 1 member.
A lot of voters, especially in rural areas, have fierce regionalist attitudes emanating from America, and local representation (i.e. "voting for your MP") is sacred to them. They will cry bloody murder when their ridings become multi-member.