2001 lincoln town car, both rear brake calipers sticking.

Check both rubber brake lines for internal collapse. You cannot see this with a visual inspection. I see this on many models after 12 years.

A quick test can determine if the problem is with the new calipers (highly unlikely) or the brake lines. Pump the brakes and let off. Crack open the bleeder valve. If fluid shoots out, you have a bad brake line. If fluid trickles out, it's likely a bad caliper. In your case the brake hoses are likely bad. The rubber hose lining degrades and can act as a one way check valve. It's easy for the MC and brake booster to push fluid through to the caliper, but the caliper return pressure is too weak to get the fluid back to the MC.