I had soil tested in 2009.
Results recommended 280 lbs potash/acre and 80 lbs phosphate per acre.
Did you apply 280 lbs potash per acre and 80 lbs phosphate per acre after the 2009 soil test?
Do you know your soil pH after the 2009 test?
In most northern North American fields soil pH is low relative to grass needs, requiring lime to increase soil pH.
If the soil pH is not within the range suitable for your grass fertilizer, even only manure, nutrient utilization will be inefficient by the grass.
While ag conditions vary enormously, the few ag studies I have read indicate returning animal manure to animal feed fields only supplies ~5% of nutrients required for OPTIMAL grass harvest.
(I understand you may only want a improved yield, not an optimal yield for three head.)
Just north of me in Florida a great deal of commercial hay is grown. Growers count on three hay crops per year. Poor years only yield two good crops. Exceptional years yield four crops. These fields are fertilized with commercial nitrogen and commercial potassium based on regular soil tests.
Tests are cheap. Supplemental nutrients are expensive. Soil pH is naturally high and natural potash is high. Excellent conditions for profitable hay production.
(Mining potash for fertilizer production is big business in eastern Florida.)
Per my seed store I top dressed a couple of times, most recently 3 years ago, by using a seed spreader on my ATV.
Did you have enough successful seed germination to noticeably thicken your grass stand?
In Florida, unless pH is within correct range and unless ample nitrogen is available to the seed, germination to green stage growth is poor. Firm seed-to-ground contact is also important, which is where a moderate weight field roller or a dedicated Cultipacker is helpful for good germination.