My friend Zoe's first boy didn't sleep more than two times 20min during the day. She obviously longed for a break during the day, but on the positive side Vasco started sleeping through the night at 4months. Something to hope for!
I think it's great that you did your strength training anyway and did it as long as was possible. She will need less engaging to be happy soon.
I was reading that all babies need more sleep than that, but sometimes you really have to help them get there. Cue the carrier!