>Wiem, co oznacza "ever", ale jakoś mi do tego zdania kompletnie nie
>pasuje, dlatego pytam...
This "ever" makes a bag of all he cares to remember about babysitting 10 year olds--the totality of the experience that he has acquired while dealing with ten year olds in his past.
The sense is experiental. Look up "experiental" if you need to.
I've just written a lengthy post about it in the thread "roznica."