Case law has in fact become slightly clearer, with this one case from 2013, which as far as I can tell through a CanLII search, is the only one that directly tackles the issue.
The relevant portion of Pinto v. Bronfman Jewish Education Centre, 2013 FC 945 (CanLII):
 Employees of BJEC’s Curriculum Development Department wrote lyrics for the 58 songs for which Mr. Pinto composed the music. The combination of Mr. Pinto’s music with BJEC’s lyrics created one artistic work, the TaL AM song. There is joint authorship and therefore joint copyright ownership, in this cohesive whole.
 As a result, subject to the issue of consent the legal effect of which will be discussed below, both Mr. Pinto and BJEC (now TaL AM) must authorize any recording or performance of the songs at issue.
That's it. While this at least provides an answer to the question that current case-law suggests Canada's joint copyright regime is a joint tenancy regime like that of the UK, it appears to be exactly one case, in a court of first instance, with no citation or in-depth reasoning as to why consent of all joint authors is required.
Addendum - a possible contradictory second case
There is a second case I found that may touch upon the issue depending on how you read it. Thibault v Tubcot & al., et Dame La-Vallee-Smith, 1926 QC CS 219 (CanLII) (Link in French, it's a decision from Quebec).
In it, the plaintiff attempted to halt publication of opera sheet music of which he composed the lyrics, by claiming independent copyright on it. The court denied independent copyright, clarifying he is a joint owner of a single copyright on the whole of the opera. Nevertheless, they still denied his motion, which could very much be read as implying a US-style tenancy-in-common approach to joint copyright.
However, pretty much all facts in the case lined up against the plaintiff in this one. One claim made by the intervener/defendants was that the plaintiff indirectly agreed to the publication. While the court didn't directly speak to this claim like they did to most of the others, they provided a general statement at the end (paragraph 14) that the plaintiff did not prove his claims while the intervener/defendants did. It's thus not clear how much precedential value this case has with respect to joint author rights and limitations.
Interestingly, the Pinto case indirectly cites this case in paragraph 138 with respect to separate composers of the lyrics and music obtaining a joint copyright on the work.