Not sure if this is a bug or a feature, but came across a Lair where Phoenix Point chars couldn’t get to the spawnery. I know it was there because a mind controlled Triton WAS able to get there, jumping up a short hop without a stair. Even with that route visibly clear, PP chars couldn’t go the same way.
And that is why I ALWAYS bring a heavy with jetpack in those missions.
With multi class, non heavy with a jetpack is also a good solution, but that’s probably what you intended say. Id say soldier with jetpack.
I love the heavy cannon 
Spawnery goes down so nicely.
But yea, any multi class with jetpack.