A very important question would be "what is the goal for the lake"? Are most anglers wanting to catch crappie or bass or cats or walleye?
It sounds like your current predator populations may be doing a good job of controlling the panfish numbers if most of your crappie are in the 10-inch range. Crowded crappie will usually measure much less than that, around 5 to 6 inches. If the crappie are very abundant and are 10 inches long and you want bigger fish then harvest a lot of the crappie. By thinning the herd there will be more resources available for the remaining fish and growth rates may improve. Keep in mind that trying the "thin the herd" via angling in a 250 acre private lake would likely require A LOT of harvest!!
Adding shad may sound good as seasonally they can provide abundant forage for sportfish. The problem is that adult shad get BIG and unusable to all but the largest sportfish. Shad can also produce very high populations densities and these densities left unchecked by adequate predation can cause problems for the sportfish populations. Shad eat plankton, same as young sportfish. Too high of densities of shad decreases available resources for bluegill and young bass and 'gills and bass will suffer.
It sounds like the panfish are the forage source in your lake. Adding shad may decrease the predation on crappie as bass, walleye, and bigger cats switch from eating crappie to eating shad leaving more crappie in the lake. Higher densities usually equates to smaller individuals and slower growth (stunting).
If you are relatively happy with your current crappie population, I would recommend harvesting more to reduce density and see if that improves your size distribution. Changing harvest strategies is much easier than trying to remove shad from a lake!! A 10-inch crappie in a Kansas lake is a pretty nice crappie, especially if you have easily catchable numbers!