So the 27.5s you tried were probably ISO 584, and the 28s were probably ISO 622. This bike most likely then had tires which would have been marked 26 x 1&3/8 . The two standards of that size at the time were for Schwinn S-6, which is now ISO/ETRTO 597, and the one found on English three-speeds, which is now ISO/ETRTO 590.
So from your description it post #4, it sounds like this is either a single-speed or three-speed bike. Does it say "Made in ......." anywhere?
BTW, you can spell out your words here. This is not a chat with a post size limit. And it's not ephemeral; people will be referring back to the information on these threads for decades to come. Readability is more important than brevity.