For the purposes of this project I will have to buy an axial ventilator
There's no reason to default to that, and good ones not to.
You'll have relatively high friction/flow-resistance/back pressure with 3" tubes - as you already know because convection isn't doing much for you.
Axial fans are in general terrible at that sort of job. Centrifugal fans are in general really good at that job. There are some weird hybrids made for duct boosting that try to get more of what a centrifugal offers packed into an in-line package, but there's no obvious reason to limit yourself to an axial arrangement when a centrifugal fan will work much better for your load.
Under the "and how do others do this?" sanity check, virtually every fan-assisted "heatilator" fireplace or stove I've ever met uses a "squirrel cage" blower - which is a type of centrifugal fan.
There's even a common variant with two blowers on either side of a central motor, which would be perfect (probably costs a bit more) for your two tubes.
Speaking of squirrels and their relatives, you might want to start by applying a shop vacuum to the 3" tubes to remove any accumulated debris (or nests) blocking airflow - before blowing that stuff all over the room.