Americast tubs have an epoxy coating on the underside and an itegrated leveling base that I havent seen before. The epoxy coating might be a bit thin at the end where its not contacting the ledger board. I would shim it. I prefer a few blobs of mortar to make up the slight difference in the subfloor over construction adhesive. Once the glue sets up its a huge pain to try to remove. The mortar can be scraped pretty easily. Both methods, I would use painters film to allow removal after the fact.
If you use putty for the drain shoe, tighten it after a day and check it again periodically for a week. Putty will scooge out over time until its done scooging.
Also, I greatly prefer a cable drain over a typical tub waste and overflow, the shoe is tightened with a nut onto a bolt rather than spinning the strainer in the tub and eliminates the potential of scratching the tubs finish while spinning.