Baby measuring big

Philly
This is my first (a girl due June 23rd). I had an ultrasound at 27 weeks because my belly was measuring ahead. At 27 weeks she weighed 3.5 pounds and was in the 69th percentile. 
I just had another appointment on Friday (33 weeks 1 day) and my belly is now measuring 36/37 weeks. She is head down and super active (even though there isn't much room left). My doctor has scheduled me for another ultrasound next week with a follow up to talk about "options". 
Anyone experience this and not have a massive baby? Or have this and was able to deliver vaginally? My ideal birth plan is as natural as possible but my doctor was already dropping hints at potentially needing to schedule a c-section. 
Any thoughts/wisdom would be greatly appreciated!

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