Quoting:
Topdressing rates may range from 1/2 to 2 cubic yards of material per 1,000 square feet.
This produces a layer from 1/8 to 5/8 inch thick.
Topdressing is best done on Bermuda lawns in mid May and June.
Core-aerating before topdressing is also a good practice.
Apr 10, 2013
(Bermuda Lawn - Artistic Landscapes)
artisticlandscapes.com
https://www.artisticlandscapes.com Landscaping Lawn
Then refining:
If done annually, then 1/8-1/4" would be ideal
(source: recent garden radio show)
Recalculating:
1cy/1000sf
Applying rates:
6000sf = 6cy
$40x6=$240 Materials
Labor $240
Lawn aeration may not be needed
(source: recent garden radio show)
If necessary, then plugs-come-out machine type = $200 rental/labor "all day"
Figures suggest the range to be $480-680
Homewyse suggests $777 after interpolation (2" to 1/4" deep)
No Frills, less than a day & you water it all in.
1/8 acre is almost DIY ....
You'll get better answers in a bit from Apache, et al.
Ten words or less ... a goal unattainable