You would also have to factor in overnight accom costs in FRA, which could increase your costs significantly.
Something worth considering if you want to avoid Ryanair and also avoid the Frankfurt to Frankfurt-Hahn issue is to fly to DUB, then either onwards direct on SAS (from approx €110 all in) or DUB-CPH on Aer Lingus (from approx €33 all in) and CPH-ARN on either FlyNordic or Sterling (from approx €30/€50 all in respectively).
Oneway flights from ORD to DUB or SNN are usually quite reasonably priced on AA, DL, CO, EI or US (starts around $210 all in). Both AA and EI have direct flights to DUB from ORD.