If Stanford recommends that you take them, I would recommend that you take them as well. I definitely understand being really busy, though.
I took the SAT IIs right before AP tests in subjects that I was very familiar with (for me, it was math and chemistry) and it ended up being a very successful "strategy." In part, this was because I didn't have much homework or ECs around that time, so I was able to devote enough time to studying. Therefore, my advice would be to take the SAT IIs in the subjects you know best at the time that is generally least busy for you. To determine which subjects were best for me, I went to the SAT Subject Practice Section
and took the online practice tests for all the subjects to see where I was most successful.
As for being in line more with the ACT, I would say that the subject tests are definitely different from the SAT I in that they test your knowledge of the subject as opposed to posing tricky questions to trip you up.
Hope this helped.