It does sound like she isn't quite ready to wake up at 6:30am but something is causing her to wake at that time. My DD is very similar, anything before 7am and she's a disaster and can barely make a decent A time before wanting a nap. If she wakes before 7 and I can't settle her in her bassinet I usually just bring her into bed and she'll often sleep for a few more hours!
If getting her back to sleep for a wee nap after a short A works, then go for it. I think if you follow EAS for the rest of he day it should be okay and she'll still have a decent routine. Maybe with good naps it will actually push her WU time a bit.