I don’t think Pasture Pro will do anything. The main chemical is 2-4-D, which doesn’t affect grass, or my clover!
Asking where you are located, your pasture upkeep methods? I mow rather high with a finish mower in my pastures. High is 4-5 inches is to keep grasses growing without shocking the plant with too much leaf removal. I cut when grasses get up about 8-10 inches or start going to seed. I prefer the finish mower because it travels independently of the tractor, unlike a brushog, cuts all grass the same length. I have nice fields, not rough or woodsy to damage the blades. But if brushog is all you have, better to mow than let grass get too overgrown.
Height of taller grasses can start shading out crab grasses that spread but have no height.
Not sure how much crabgrass you have, but some garden friends paint on glyphosate (wearing protective rubber gloves, total body coverage) directly on the plants using sponge brushes. They have immaculate lawns and gardens! A bit of overkill for me!!
I would try ignoring the crabgrass, plant some other types of grass in those areas, see if you can shade it out. I would NOT stir up the soil, just scatter seed and cover the area with dirty bedding, sweepings from your hay storage, a bale of straw scattered about, some dirt you might have on hand. Cover prevents seed washing away, helps keep the dirt moist to sprout the seed. I have crabgrass come up every summer in the hard use barnyards. No green all winter, it is eaten, but by midsummer it comes back to cover the mud/dirt. Gets mowed when I cut the weeds in there. I really don’t have it anyplace else except the hardest used areas, gateways. Better crabgrass than other weedy plants!