The team of Negro Leaguers that toured Japan in 1927 was drawn from the Philadelphia Royal Giants club in the California Winter League of 1926/27. This team’s roster featured no less than six Hall of Famers: Turkey Stearnes (.387 with a league-leading 8 home runs), Bullet Rogan (6-2 on the mound, .328 at bat), Willie Wells (only .181, 19 for 105), Biz Mackey (.316), Bill Foster (6-0, with 49 strikeouts in 55 innings), and Andy Cooper (5-2). The Royal Giants won the pennant (of course) with a 26-11-1 record against three white teams composed mostly of a mix of major and minor leaguers, along with a handful of semipros. This was with their fourth-best pitcher, George Harney (a decent but not great knuckleballer from the Chicago American Giants) leading the team with 116 innings pitched (Cooper had 71, Rogan 68, and Foster 55).
I think you’d have to say that this would qualify as one of the great Negro League teams of all time. Rob Neyer, in his book Baseball Dynasties (co-authored with Eddie Epstein), picked the 1934-36 Pittsburgh Crawfords as the greatest Negro League team of all time, largely on the basis of their having five Hall of Famers. However, one of those, Judy Johnson, is kind of an imposter and was well past his prime by then, anyway; Oscar Charleston was still a very good, even great, hitter, but was in his late thirties; and Cool Papa Bell was certainly very good, but his reputation has probably been a bit inflated by anecdotes and hyperbole. This leaves Satchel Paige and Josh Gibson, legitimate all-time greats in their primes. While none of the Royal Giants’ HOFers could measure up to those two, they were, on the other hand, nearly all in their primes (Wells was a little young, and Rogan was just past his peak, but still excellent: he’d be the Monarchs’ best hitter and pitcher in 1928). Cooper was probably the worst of the six, and he was a fine pitcher for many years, certainly as good (IMO) as the Crawfords’ number two starter, Leroy Matlock. A series between the two teams could be awfully good, but I think there’s a distinct possibility that, as Bill James might put it, the Royal Giants would beat up the Crawfords and steal their lunch money.
(Neyer and Epstein were looking for teams over three to four-year stretches—thus the title Baseball Dynasties—so the Royal Giants wouldn’t qualify, as the California Winter League teams were ad hoc affairs with rosters that shifted quite a bit from year to year.)
After the end of the California season, the Royal Giants’ owner/promoter, Lonnie Goodwin took about half the squad to Japan, including Mackey, Cooper, Rap Dixon (.349) and Frank Duncan (.276). The rest of the club, including Rogan and several of his other Monarch teammates (Newt Allen, Dink Mothel, Newt Joseph), barnstormed their way back east to Kansas City in time for opening day.
The name “Philadelphia Royal Giants,” by the way, didn’t (as far as I know) signify any special connection to Philadelphia (other than Mackey being a Hilldale star). The 1930/31 edition of the team (28-2-1 against probably weaker competition than the ‘26/27 team faced) also featured six eventual Hall of Famers: Mackey, Wells, Foster, and Cooper, plus Mule Suttles and Jud Wilson. Rounding out the ‘30/31 roster were Rap Dixon, Newt Allen, Vic Harris, Chaney White, and Chet Brewer, all very good Negro League players.
My information about the Royal Giants comes from William F. McNeil’s excellent book, The California Winter League: America’s First Integrated Professional Baseball League, a great contribution to Negro League history. The pedant in me, though, wants to point out that the subtitle should really be “North America’s First Integrated Professional Baseball League,” since Cuba is part of the Americas, and the Cuban League was integrated in 1900.