Thanks for the great website! I will certainly try some of the suggested remedies. I would also like to share some of my experiences.
First of all, I'm NOT constipated. My bowel movements are remarkably predictable (daily, usually early morning) and strain-free. However, afterward, the hemorrhoids usually appear and will remain distended for hours UNLESS I perform my post-BM "ritual", which consists of lying face down on a flat surface and relaxing completely. I remain in this position for 5 or 10 minutes and during that time I can usually feel the hemorrhoids retract, after which I'm good to go.
This doesn't always work. When it doesn't, I apply a small blob of a product called Desitin. Sorry, I know I'm not supposed to submit product names, but this one is not widely known and is God's gift to hemorrhoid sufferers. It comes in a tube and is a white ointment containing zinc oxide. It won't cure the hemorrhoids, but it makes them a lot easier to live with. Don't confuse it with your toothpaste!
Another thing that has helped a lot: several years ago I visited a friend in Thailand. In that country and, I assume, many other Asian countries, most of the bathrooms are equipped with hoses that are used to clean the rectal area after a bowel movement. They are similar to the sprayers found on many kitchen sinks in the US, and those can probably be adapted for this purpose by a competent plumber or do-it-yourselfer. I brought one back with me from Thailand and I use it to clean up after a BM, followed by lightly patting the area dry with toilet paper. This is MUCH better than wiping with dry toilet paper, which just causes irritation and bleeding. You can also buy toilets with built-in bidets which serve the same purpose.