Hi Joe, you are having a continuous problem with crabgrass because of its seeds. The plant germinates, goes to seed, the seeds remain in the soil and then germinate the following year again. Its a continuous cycle.

Using the sod cutter will disturb the soil and bring more and new additional crabgrass seeds to the surface to germinate and the cycle returns.

I would delay the sodding a while and fallow the soil. Go ahead and remove the old grass with your sod cutter ASAP. Prep and amend the soil as needed per a soil test. Then fallow the soil. This means watering deeply and frequently. Fallowing will germinate any weed seeds in the soil. Frequent sprinkling germinates weeds.

After 2 to 4 weeks you will have nice salad greens growing so spray the area with Round Up to kill the new unwanted growth.

Now you have 2 choices. You could go ahead and lay the sod, or if you want some extra insurance, fallow again another week, spray Round Up one last time and then lay sod.

Another option is "solarization". But you need more time and high sun and temperatures for it to be successful. See link below.

This probably is not what you wanted to hear but in most cases it is better to take the little extra steps and do it right at the get go, rather than a common contractor's cheap and fast job, which will then give the long lasting results (ergo weed free) you are looking for. And actually, the fallowing only adds a $9 bottle of generic Glyphosate and a few extra weeks to the project.

Here is a link that might be useful: SOIL SOLARIZATION

Crabgrass is very easy to control in St Augustine. Here's what you do.

1. Water deeply and infrequently. If you have an automatic sprinkler, set it to water no more frequently than once a week. Water for an hour and see how long it will go. If it starts to wilt before a week is up, then water longer next time. Frequent watering will sprout all the crabgrass seeds.

2. Mow at the highest setting your spouse will allow. St Aug thrives up to 30 inches long so you can't make a mistake except going too low. I mow at 4 inches. Why? Because tall grass provides too much shade for crabgrass seedlings to take root.

3. If you still get some crabgrass, it is trivial to kill the crabgrass and leave the St Augustine untouched. St Aug is highly salt tolerant and crabgrass is not. If you dust baking soda on damp crabgrass, the crabgrass will die in a day or two leaving the St Aug to thrive.