There are ways to minimize changing tiller. Newer bow makers especially have this problem where they get a bow that seems to shoot ok but then gets weaker and weaker.

A couple things to consider-

The bow should be tillered well. Any weak or overly strong points shifts energy storage away from where it was set initially. Also if you want a 40 pound bow at 28 inches, tiller the bow to 40 pounds at 27 inches. Then sand and finish as normal. The bow can lose a little poundage as it takes its final set and you end up at the poundage you wanted at your draw weight.

Bows are way easier to be accurate with. Especially a well tuned bow. There is little comparison to the sling.