It is a fun exercise.  I feel that psychedelics have changed the way I think about infinity, and thinking about infinity almost always puts me back in a psychedelic mindset.

I agree that the sum of infinite sets is not hard to conceptualize, but I wouldn't call it the ultimate infinity either.  Closer to the ultimate infinity would be the sum of infinite sets of infinite sets, and even closer would be the sum of infinite sets of infinite sets of infinite sets... The end of that progression is something that the mind can converge on but can never reach.  There's a cognitive asymptote there that, like you said, points toward something.

My understanding of the difference between eternity and sempiternity (and it is a vague understanding) is that sempiternity pertains to all of time, whereas something that is eternal exists outside of time.  For example, to experience throughout all time would be to be sempiternal, but to be able to step outside of time and see all of sempiternity as one big picture is to exist in eternity.  Another way to think of it is that something that is eternal is timeless.