My DD went through the same thing right around 3.5 years. For her it was naps also. She was in daycare a few times a week and I told the daycare provider that she wasn't to nap for more than 20 minutes. She would fall asleep after lunch at the appointed time and they would wake her up after 20 minutes and she would play quietly in an opposite corner or read books, etc. What a difference that made! I could always tell if they forgot to wake her up after 20 minutes because she'd be up until 10/11 that night. I hear you about not wanting to give up nap time - maybe shortening the time and making sure it's earlier in the afternoon? Now that the weather is warmer lots of outside time running around in the late afternoon might help too
Good luck!