I'd mix it in in the top 6"

I was told most soils can only handle 3 tons/acre per year of lime max.-
I'm sure they want you to keep the lime in the upper few inches of soil for best effect this year.

Truthfullly you'll need a couple years before the soil is changed to a point that you can grow clovers easily.

Iron clay peas might grow this year - but its not a sure thing. Rye, oats, corn, even soybeans can grow OK in Ph of 5.0 to 5.5.
I'd put down the 6000 lbs & concentrate on an an annual this year - and re-test in the spring if it were me.

FH