Yet no collectors McKee knew had ever heard of a card set showing the team.
In 1992, that changed.
Dan the elder was at a Sotheby's auction in New York, trolling for oddball cards, when he realized a consigner was offering a set that showed 14 of the team's 16 members.
It was printed by Alpha, a long-defunct company described only briefly in the auction catalog. For reasons unknown, it didn't include Keeler, the team's biggest star, or backup catcher William "Boileryard" Clarke. But the rest were there.
The cards were the first ever made for some of the players, including Keeler. That made them "rookie cards," a genus that exploded in value during a collecting boom in the early 1990s.
The set failed to meet its reserve price of $3,000, perhaps because collectors had no idea it was coming. The consigner sold the cards separately to others around the country.
McKee's appetite was whetted, and he kept watch.
"They were one-of-a-kind. They included many great players. But most of all, they represented 19th Century Baltimore Base Ball — and I do mean 'Base Ball' with two words," he says, referring to the accepted spelling of the time.
This, he thought, was a set worth assembling.
Over the next decade, he went after each card, acquiring them one nervous deal at a time. He never paid more than $2,500. By 2002, he'd spent $30,000 and owned them all.
"I felt — complete," he said, a grin spreading below his close-cropped mustache.
Later that year, another hobbyist, W. Thomas Lawrie, decided to write an article on the set for a collector's magazine. He spent weeks researching the Alpha company. His work was a window on history.
Lawrie believes that Alpha took the unusual step of printing just the single set so it could place the cards in a display window when the city was in the grip of pennant fever.
"Look closely and you'll see a minor strip of damage at the top of the backs of [most of] the cards," he said. "It's reasonable to guess that those correspond with tape."
McKee loved the cards so much he'd often pull them from his safe and stay up late studying them. But eventually he had to weigh the value of his love. In 2006, a New York collector approached him at a card show and made him an offer he couldn't refuse.
He would not name the buyer or reveal the specific price, but said it was a six-figure amount large enough that he could finalize the purchase of a home worth more than $700,000.
McKee, who had figured the set might be worth $40,000, was stunned.
He later learned the man was keenly interested in vintage rookie cards — and that the sum meant little to him.
"It meant a big change for us, though," said McKee, adding that he was reluctant to sell, even at that price.
Lew Lipset of Old Judge Vintage Cards Auction in Arizona, a longtime dealer, said he might have guessed the set's value to be closer to $6,000 per card, or $84,000 total, but added it wouldn't shock him to learn that they'd sold for much more.
"It's very hard to set a real market value on a one-of-a-kind set," Lipset said. "It's worth what a buyer thinks it's worth."
The New York collector eventually sold off some of the non-Hall of Fame cards. McKee reacquired Gleason, Hemming and Reitz for about $2,000 each.
The New York investor recently emailed McKee to give him first crack at the Alpha Hall of Famers he has decided to sell. He hasn't named a price yet.
McKee's sure the cards will be out of his range now, but he'll make an offer just the same. It would be great to get the old set together again.
"The Alphas were my pride and joy."