The phrase "A creature burning in this way never takes more than 2d6 points of fire damage in a round" in my opinion can be read "In a round a creature never takes more than 2d6 points of fire damage from burning in this way" without violating RAW. In such an interpretation, this line most likely talks about the following:
Same Effect More than Once in Different Strengths
In cases when two or more identical spells are operating in the same area or on the same target, but at different strengths, only the best one applies.
Even without Mortalbane, you theoretically may benefit from two Brimstone Blasts on the same target, as the best roll would apply each time (note, it still isn't greater than single Brimstone Blast's possible maximum damage).
In particular the line you have quoted makes the above rule relevant even if two or more warlocks hit you with Brimstone Blasts (or the only one present delays). Would it be Vitriolic Blast each would tic on a different initiative count so there is nothing to compare in strengths. But with that line new Brimstone Blast can't make you catch fire again - you are already burning.
(Maybe you may still take damage equal to the difference between two burns if the second is higher, but I don't think it was intended to require that level of complexity.)
It is hardly intended to limit what you can do with a single use of an ability, so Mortalbane Brimstone Blast should work fine (and I believe only once per blast, but am I right or wrong on this is irrelevant for this question).
Critical hits are a different issue. Brimstone Blast effectively applies a status to the target (target is burning for X damage). Even on a critical hit it will apply just the same status, so the damage won't be multiplied even were it a straight number not a dice pool.