Also went in April and, from talking to staff/drivers/guides/etc, I would be quite wary of visiting in May as the heat peaks. We really enjoyed visiting in April as most monuments (especially in Agra) were relatively hassle-free compared to high season, i.e. fewer crowds and less scams/touts/etc. The only truly hot place we visited was Jodhpur (40-45 during the day), but touring in morning/evening was fine.

We skipped Aman-i-Khas precisely because we feared the summer heat in such an outdoor-oriented thing, and it really cleared up the logistics of getting around without too much time in cars/trains. Amanbagh is truly not to be missed, however. GM Harish, Chef GNB, and their numerous staff are doing a fabulous job, our favorite Aman experience in recent memory!