Failed to route the following signal

Using an ASIC is usually based on a whole other set of requirements(volume, pricing, power, speed, and if you have the tools/expertise to develop an ASIC). And note that just having a lot of LUTs/Reg doesn't mean it will use a lot of routing. It's the everything talks to everything nature of this design. In this case, it just means you may need a larger part or something like that. Also note that Stratix series should have more routes available, so that's another option.