The second-generation Genesis is an excellent car but it's not an exciting one. What you enjoyed about the Lincoln you might enjoy about it. Even in R-Spec form the first-generation Genesis doesn't ride or handle nearly as well. Reliability of the last few years of the second-gen Genesis also hasn't been great.
What do you dislike so much about the ILX, that you didn't dislike about the Civic? Did you get a powertrain other than the 2.4 + manual? That could be the problem.
The Mustang suggested above could split the difference pretty well. Still a bit large and heavy for my taste, though.
Two other coupes that might work are the Infiniti G37 (also offered as a hardtop convertible and as a sedan) and Hyundai Genesis Coupe. In both cases the ride might be too firm, but worth a test drive.
It's a bit of a reliability risk, but the Cadillac ATS is the best-handling compact sedan, so I'd also test drive one of those. A 2014 might avoid some first-year issues, but might also be harder to find in your price range. The 2.0T + manual is the most engaging to drive.