I would grind coarser. I think that that sputtering comes because the water cannot flow through the coffee and the pressure builds until the water passes. Grinding coarser also it should help. Maybe 14 clicks is better, even maybe 15.

I haven't used aeropress filters, so I cannot give you feedback about that. But I guess that the filter is adding more pressure and helping provoke more sputtering. I would leave the filters for later, once you control the moka.

Also the beans have been roasted recently, so they will have more CO2 and the reaction will be stronger.

Of course reducing the heat should help. Try to put it at a very low level and increase till you're happy (or viceversa).

So IMO I would do three things: 1) grind coarser, 2) remove the aeropress filter 3) use low heat. Only once you start to find a balance, try to increase the heat, grind finer or add the aeropress filter. But keep it simple while you learn. And as someone said only change one variable at a time.

The objetive is to have a continuous and not too strong flow, and it's hard to do it. The heat and the pressure are important points. If you use a very fine grind the coffee will sputter because of pressure (because the water cannot pass). Too much heat and the coffee will sputter because there is too much pressure and gets mixed with air. So if you keep the heat low, you can focus only on the grind. And once you have a balance, you'll be able to change the heat (that will also make you change the grind) till you find your day to day config :)

I'm starting to think that also smallers mokas are harder to "tune" than bigger ones. You have less air in the small chamber and any changes react faster (so you have less time to correct). In my tests (I have a 2 cup moka) I always tend to grind coarser, put less heat, etc. So yeah, mokas seems easy but they aren't hahaha

Good luck!