On the subject of the power problem, have you checked to see if the secondaries are opening at all? It sounds a lot like you are running just on the primary bores, or have a very gradual and sluggish secondary. That would make poor power and response when you floor it, but wouldn't necessarily pop or sputter because the air/fuel is still correct, you just don't have enough of either to make for good acceleration because you are effectively running a small two barrel carb. .
That would be true if the same main jet(s) serve primary and secondary chokes. If the primaries have main jets unique to them, then if the secondaries don't open the air flow through the primaries will be much higher than intended but the (primary) main jets won't be big enough to keep up.
Alternatively, once the airflow limit of the primaries is reached the airflow is 'choked' and if the point of fuel entry is downstream it will be subjected to significant vacuum and if the main jet can flow enough, the mixture will go rich but probably un-noticed as the principle symptom is lack of power due to being starved of air.
Does the carb in question have emulsion tubes?