I decided to use this as an opportunity to compare the yeasts side-by-side, rather than mixing together. Interestingly, during the time that I had the two yeasts rehydrating, the 34/70 foamed up nicely, while the M-84 did next to nothing. Interesting, I thought, but didn't give it a second thought. I put both LBK's into the lagering fridge at about 50* F.
It's 24 hours later, and the LBK with Saflager 34/70 has built up a decent base layer of krausen. Not a raging, violent fermentation by any means, but this is lager yeast we're talking about -- slow and steady wins the race.
The Mangrove Jack's LBK? Hmmmm.......pretty much nothing.

I have since read on other forums--and this one--that a lot of the Mangrove Jack's strains are slow starters. In fact, someone wrote that they had to raise the temp on their M-84 after two days to get it started.
So, I've taken that LBK out of the fridge to let it warm up a bit, and will hope for the best. Since I don't have any other lager yeast on hand, in a worst-case scenario I'll have to pitch some ale yeast (US-05 or Fromunda) to make a "Bavari-ale." At least I know the other half of the batch is proceeding as planned.
Yeast. Can't drink with 'em; can't drink without 'em. Or something like that.