Thanks everybody for the tips. I finally got it done. The most difficult part was getting the old bolts out.
On two of the bolts, I was able to grab the top with vice-grips and turn the nuts off far enough to then grab the bolt under the nut with thin vice-grips and finish taking off the nut.
On the third bolt, I couldn't get anything under the nut to grip the bolt while I tried to remove the nut, so I ended up using a hacksaw to cut the nut. Boy, that takes a long time with only 1/2" of travel on the saw.
The fourth nut was a bugger. I couldn't get the nut to move at all on the bolt, so I had to use a dremel tool to cut it off. For those of you familiar with the base of the toilets, I could only get the dremel tool in to cut the nut vertically. I had to cut both the nut and the bolt vertically, then turn the nut and bolt, make another cut and slowly break the nut off of the bolt.
The installation of the new was easy. The rubber washers on the heads of the bolt actually kept it from turning while I tightened down the new nuts.
Based on all of your feedback, I did come up with a plan in case I had to keep the bolts from turning while I tightened the nuts. I bought extra nuts so that I could thread the first nut on and get it as tight as possible. Then, to keep the bolt from turning, was was going to put two additional nuts on at the top of the threaded end of the bolt, tighten them together ("lock" them together), then use a wrench on one of them to keep the entire bolt from turning while I tightened the bottom nut. Nuts, that a lot of nuts.
Fortunately I didn't have to do this.
Anyway. all's well that stays in the "well".
Thanks for your tips.