If you seed now all the seed will die.

If you rototill you will bring up new weed seed that you never knew you had. That seed will sprout when you put out the new seed.

If you rototill (anytime) then in three years you will have the bumpiest lawn on the block.

Sod is your only grass choice for now. If you can get by on mowing weeds, then in August you can start thinking about doing this job right. Spring was a mistake - just as rototilling is a mistake. Perhaps you got both those pieces of advice from the same magazine article.

As for your soil test, Google "logan labs soil test andy". Andy is a guy who is expert at reading Logan Labs tests. Don't look for the first hit or two. Look for the most hits to the same website.

With your water rates you might look into alternative grasses. Specifically, look at the wheatgrass varieties available in your area as well as blue grama. Most of these are bunch grasses like TTTF but they are native to the prairie. As such they hardly need any water or fertilizer. When you mow them they can look like this...

{{gwi:79340}}
The strawberry clover in the picture was done on purpose. Otherwise the turf is dense enough to resist weeds.

Thanks for the advice!

I'll consider those other species.

I don't care about the species per se, other than it must be highly neglect resistant, have , nice barefoot feel, and be green (pref. dark, but not critical) . We do have a fair amount of cutworms and moth things in our local lawns, so the endophytes of the TTTF seemed useful.