Very nice! Those are great looking boats.
A model that large won't be cheap. You don't say what the hull is made of, I assume it's a 3D resin print. I don't know if the technology fits with your plans but high density foam would make for a lighter and possibly cheaper (depending on set up cost) model. There was a crowd in the US making a range of multi-media Napoleonic ships using this as the basis for the hulls, which meant that even a frigate was viable, albeit somewhat pricey.
For me a brig-sloop, somewhat larger than your cutter would be my ideal. They were ubiquitous for independent work, could be used for the entirety of the Napoleonic Wars and also into the 1840s making it useful for things like anti-slavery patrol games. It's also about as small as you get where you can still deploy a Royal Marine detchment.
One other thing. I'd ditch the rather idiosyncratic version of 'Barbary' lest people think you are referring to an invasive plant species or folk in China making knock off trenchcoats.
Overall it looks like an excellent project. Make it and the people will come.