For the benefit of anyone coming here on down the line (pun intended), we had a very good experience with Amtrak's luggage storage service at DC Union Station. We arrived at about 7:10 am, followed the signs to Gate A, and the baggage storage area was well signed and easy to find. If you need specific directions, it is on the right as you approach Gate A, opposite the men's room.
There was someone there to take our bags when we dropped them off, and someone there to return them to us when we went back about 1:30 pm. They only accept credit cards. A door in the counter opens so we were able roll our bag through and did not have to lift it up and over the counter.
The signage clearly stated $10 if you had an Amtrak ticket and $20 for non-ticketed passengers. The sign also said they open at 6:30 am. I don't remember what time it closed, although the link in post
#6 above says 9:45 pm.
Please note this is to store and retrieve your bag to take it with you on the train, NOT for checking luggage onto the train.
Thanks to everyone for your tips, advice and comments. We had a really nice ride home on the train, and it was well worth the $ to leave our bags in the station during the day when we were out and about. A painless process all around.