Are we to believe that days existed before planets and stars existed?
I don't, but apparently the author(s) of Genesis did.
Or that God was somehow limited in his power to create existence in an instant and have to create it over a matter of "days"?
That seems to be the intent of the author of Genesis 1, since God had to rest on the 7th day. That sounds like a limit.
Or extrapolate that humans lived alongside dinosaurs?
What do dinosaurs have to do with Genesis? The author of Genesis didn't know anything about dinosaurs.
And on top of that, which creation account are we to choose?
Well, there are certainly two given in Genesis. Choose whichever one you want, or accept the truth of both.
Genesis 1-11 is actually considered what is referred to as mythological writing. And by that, I do not mean that it is a myth -- I mean that the writers wanted to convey theological and philosophical truths without much care for obeying historical or scientific laws. They were more concerned with conveying truth than historical or scientific details.
The authors wouldn't have differentiated between theological truths and historical truths as we do, and scientific laws or details simply didn't enter into the discussion, as they had no conception of "science."