Bottling in 2L PET

I am doing small batch BIAB (2 gal ) indoors during the winters now and bought a carbonator cap.
I intent to use either 3-4 2L bottles or a few 1L’s to “keg” my trial 2G batches using the cap to add CO2.
My question is for anybody keen on math or prior experience doing this specific function.

I tried doing an extra bit of my last 5G batch into a 1L and added CO2 via cap to cold wort for about 2-3 days at normal keg pressures of 11-12 PSI.
Although it had some carb it didnt seem fully carbed, do I need to keep 1 or 2L bottles on gas 1-2 weeks like my 5 gallon kegs to get proper CO2 in solution or should it only take 1-2 days each time I want to carb up to fully saturate the CO2 to 2.5 ish volumes I would like.

Also I understand well I could play around with 20+ psi etc… But I like to set my “kegs” etc… to normal serving pressure to ensure correct carb everytime not high/ low depending on.

Yes it just needs more time. Its not the volume of the beer that counts but the volume of CO2. 2.5 volumes of CO2 is 2.5 volumes regardless if its 12 oz or 640 oz. If it were bottling conditioning would only take days.

I do the same, carbonator cap with 2L bottles, and it takes the same time to carb as my kegs. I use the 2L bottles to get an ‘express sample’ of the beer but I have to do as you alluded to, crank up pressure and shake. Seems to work out pretty well though since I make sure my kegs are sealed with 30 psi, at the same time as doing that I shake the 2L bottle with 30 psi CO2 hooked up, disconnect it and throw it in the fridge. That seems to get me pretty good carb in a day or two.