DKIM records are just DNS TXT records. Do they have a limit on the size of TXT records? Or are they going out of their way to try to parse the TXT records you're adding that look like DKIM records, failing on them, and then refusing to add them?
"first 255 bytes" "second 255 bytes" "etc"
DNS clients combine the 255-byte strings back into a single string.
No, DKIM clients and SPF clients do that. Generic DNS clients, however, are in theory free to ascribe any semantic meaning they like to the string separations.