Heat the keel bolts with a torch. The nuts will usually remove farily easily. If my experience ('74 C26) is any indicator, you'll find the bolts coming out of the keel in pretty good condition. You should replace the backing plates. Use Steel bar. Most of the bolts coming out of the steel keel are steel ... not stainless. Use steel bolts to replace the corroded ones to avoid different noble metals. You can glass over the new bolts and backing plates to reduce corrosion (I didn't do this and I have new corrosion around the bolts about 10 years after I replaced them in 96).
I'd not try to "drop" the keel unless you can identify leakage around the keel (not likely). If there are cracks in the gel-coat around the keel plate (you'll see this from the outside hull view), you can carefully grind the bad gel-coat and packing away and patch it with glass roving and epoxy where needed. Good luck.