I would like a small internal filter with long periods between cleanings so the filter will work as a good biological filter
I would like that too, but the very best way to expand times between cleaning is a bigger filter. As you wrote yourself, after a certain timeperiod, any filter will work biologically. This will result in much larger episodes between ceanings.
Personally, I have internal filters measuring between 5 and 10 % of the total content of their tank, and these can almost do without cleaning for a year. In fact, I have installed some 12 of these filters 2 years ago (tis week 2 tears ago) , only working with the well known blue mattrasses. I think I have not rinsed half of the mattrasses, but onty 2 out of each 5.
Besides, I hardly rinse them, because I squeese them two or tree times, than I let them oxidise in the air, and after 3 months they are almost clean. I squeese them another 2 times and they are ready for use.