Please don't call yourself an idiot-- you'r just "busy" with other stuff.
I would be careful about changing the grade of your yard in such a way that it slopes towards your house and causes moisture problems. If it looks like you can dump more dirt on the gravel without changing the slope, or raising it too much, go for it.
In my climate, (PNW) I have not found chickweed to have aggressive roots. The seeds just seem to pop up easy, but I think they need light to germinate (sorry about my spelling). If you can pile the dirt deep enough, and get the grass seed going it should overtake the chickweed just enough to be servicable (only astroturf is perfect). Is there a landscaper or someone you can call to check this out, and see if they think this would work?
That is what I would try, but I admit that I tend to garden and learn about gardening by making mistakes and trying again
Please be gentle with yourself, your baby has been a HUGE project I'm sure, your not an idiot, your BUSYMOMMY!