You're highly intelligent Feelhorriblyguilty... you are aware of the problem .... so you ARE dealing with it by being aware of it (if that makes sense)
We're all screwing up our children in one way or another ... as a parent ... it's a given
It's taken me a while to get my head around the fact that Him Upstairs has blessed me with a child who is different to me in many ways, so I know where you are coming from! (I'm fairly introverted/bookish and hopeless at sport. My 5 yr old dd on the other hand is outgoing, socially very confident, very coordinated, and loves dance, sport and music.)
It's not always easy but the way I'm trying to tackle it is by trying to think of it in a different way; ie instead of it being a "problem" I'm trying to focus on the benefits it can bring to both of us.
She's challenging many of my rather rigid and pre-conceived ideas that I have about life and in turn I've had to look at myself a lot harder (this is one of the greatest gifts dc give us I think - without sounding too saccharine). She is leading me down lots of different routes that I wouldn't normally be treading. (I've started exercising for example!!)
Also, it's good for her that I have different skills. My dd may come to appreciate books and reading later in life and if I was sporty and the same as her she wouldn't have that extra string to her bow.
(Eg, my parents loved gardening but I showed NO interest in it as a child! Thirty years on I am as green-fingered as they come!! Things rub off!!)
A person much wiser than me once told me that as long as you follow the three main rules of child-rearing you can't go too far wrong:
Rule No. 1
Love your child = most important of all
Show your child love
Love them for who they are as an individual
Rule No. 2
Stimulate your child
Stimulate your child to develop in the way that it wants to develop
Rule No. 3
You are the parent
Be clear (and feel comfortable) about the boundaries/limits within which you allow your child to develop
I think you need to take a step back perhaps and just try and think of the long term view. She's only 7! She has all the time in the world to develop other interests and some of your academic prowess may well rub off on to her. Think how great it will be if she is sporty AND has a good academic grounding.
If you don't mind me being frank, I think you may have hit the nail on the head when you raise the issue of her being an only child. I think this may be more of an issue than her current lack of interest in books/academia. I know myself - it's not always good for dc to have the bright white heat of a concerned, mother (however loving) focusing solely on them.
So BE a bit more selfish. Concentrate on your own interests a bit. Take some time for YOURSELF!! Be a bit more "neglectful" of her (iykwim).
On the patience issue - I sympathise - I have turned out to be a loss less patient than I thought I was. I'm still struggling with this one but my overall advice would be :
Relax! Step back! Follow her! She will lead you in the direction she needs to go.
She sounds terrific! AND you are doing great! You really are!