I have done a lot of the sort of work you are attempting. In my case, nearly all commission work with hard deadlines. Lots of pots and/ or tiles with sprig (2D relief) work on them. So I know.
Always pressed for time, seemingly. Racing to get things made, so they can dry as slowly, and as completely, as they need. In this regard, I find myself throwing pots, or making tiles and then when they are barely stiff enough to be handled, pressing and pulling out the sprigs from the molds and applying them on to the pots, or tiles when everything is still quite wet. I use a wire brush and score both sprig bottom and ware body. I make two passes of scores, at right angles of each other. Dabbing a drop of water into the score on the ware, to displace air bubbles and to help further seal the bond, I will then place the sprig on. Then, this is important, I always wipe my fingers, quickly, and try to get them as dry as I can. I found that pressing the soft wet clay sprig on to the pot does very little deforming if the fingers I am using to press with are dry. Try it.
As for thick sprigs, especially on pots that can’t have pin holes through their bodies, stabbing with a pin tool into the sides of the sprig, parallel to the plane of the tile, or pot, but not into the area of the scored bond, works great and allows it to out gas any residual moisture just fine.
These deadlines, they are sometimes a beast! I have been known to sprig 40 pots in a sitting. Knock on wood, I have only had three sprigs ever come off and one blown off, and that out of thousands of pots and tiles. At the time, I noted that friends don’t let friends sprig at 3 am in the morning. I got sloppy and didn’t score with my usual care. Anyway, those particular pots were fired artfully tipped over enough to, I hoped, to keep the sprigs from sliding and I did succeed in fusing the sprigs back on in the glaze fire. And, I made deadline, got paid, and all is well.
Best wishes that everything goes well for you and you make deadline.