Harrington's Ice Cream Baseball Cards issued in 1927 and 1928 theory
 

Just my thoughts and reasons are Loyd Waner, the only player out of the set made his debut April 1927, John McInnis & Rogers Peckinpaugh last season 1927, Stanley Coveleski last season 1928. Only one player's last season in 1925 was George Burns. I would think the company would have issued the cards during the summer months starting around late June so they had time to get photos. Also the variation on the backs, differentiating 1927 and 1928

I don't collect Harringtons so take this for what it's worth, but I doubt they were issued in 1927. As I understand it, the Ice Cream issues parrot the E210 York Caramels type 2 set. York Type 1's are attributed to 1927, and have several different players than what was swapped out in Type 2 (which has Gehrig and other Murderer's Row Yanks not in the '27 set). Unless you have a Harringtons that matches up with Type 1 only, then it seems like they follow the Type 2 Yorks, which are attributed to 1928.

My understanding of the differences between Type I And Type II are a glossy finish and the backs are different left or right for 1927 and 28

Those differences are there, but there are also many different subjects in the Type 1 York Caramel set, which, for example, does not include Combs, Gehrig, Lazzeri & Hoyt.

There are collectors of these sets (and W502) that hopefully will chime in, but it seems clear that one set's checklist preceded the other. Maybe they were both issued in 1927, one set updating the other, as I discovered with the m101-4 and m101-5 sets from 1916. Either way, it still seems like the Ice Creams match up with the Type 2 Yorks and were issued later.

Walter Johnson's last season was 1927, and he is not included in the Harrington's set, the other F50 ice cream card sets, or the first W502 set. It is inconceivable to me that Harrington's would have issued their card set in 1927 without including WaJo, especially as WaJo is included in the York Caramel Type 1 set. And, WaJo is not in the York Type 2 set, which is now attributed to 1928.
Val

It could have been what photos they had available or were able to obtain for example Babe Ruth photo reused since his days with Boston. Also the set has one of the biggest players Babe Ruth along with Ty Cobb then with the A's