I would try the other easier option on the list and only if those dont work would I start excavating my yard busting gas pipeline trucking in topsoil etc.
You could bring it in 1inch per month over a year. or you could bring in straw and
compost it compost it.
You could also go for a meadow lawn. Or you could switch over o white clover, it only get to a height of 2-4inches and it makes it own nitrogen.
So less/no mowing or fertilizing.
Or you could go all out and plant 10ft tall fruit trees instead of lawn.
Here is a huge list of manageable fruit tree you can plant.
http://www.onegreenworld.com//index.php?cPath=1
Iterations are fine, we don't have to be perfect
My 2nd Location:Florida HardinessZone:10 AHS:10 GDD:8500 Rainfall:2in/mth winter, 8in/mth summer, Soil:Sand pH8 Flat