To get a smooth print on these you need to "bridge and build" with your ub. The first pass is critical, it needs to matt down all the ringspun fuzzies and it must fill in the natural peaks and valleys of the heathered fabric, prepping the base for the top colors to finish the deal. Similar concept to face coating a screen in a way.
We have success with 135/48 or 150/48 coated 2/1 or 2/2 round. Hard fill and light pressure on that stroke with a sharp blade.
Keep that pressure absolutely minimal on the UB screen, make the fill do the work and the squeegee just shears over that stencil, dropping out the ink. Once that's down, it's all up to the mesh and EOM, provided you have a good LB white in there. We use WFX Epic Quick but there is a similar version of this ink from probably every company. I'm not an auto printer but I think the exact same concepts apply here. The last thing you want to do is drive ink down into this fabric, it gets you nowhere and the stiffened hand of your print will be extra noticeable on such a soft, easy draping fabric when it's worn. You can up that pressure on the top colors if the base is done right and, as mentioned, flashed correctly.
They do discharge surprisingly well but I don't think this solves the nappyness issue for you. Discharge will help with reducing the appearance of fibrilation by way of dying some of the fibers that might poke up out of the print but if you are aiming for a smooth top surface this won't help to that end very much at all. Maybe discharge + a very heavy deposit of one of those HSA type wb inks up top would do it, couldn't say as nobody wants to sell me any HSA for some reason.
I could def see a smoothing screen helping out for this.
Best approach is for a semi-transparent look right from the artwork on these, which is not only easier to print but looks great. The above is my best recommendation for a smooth, opaque print with a larger image area. End game here with plastisol in this exact scenario is going to be thick but smooth and soft, rubbery feeling imprint.