As a reminder, you can now use Luau binary buffer type (Introducing Luau buffer type [Beta]) in MessagingService data.
It still has encoding overhead (35 + math.ceil(bytes / 3) * 4), but buffers up to 741 bytes should be possible.
Encoded length can be checked with HttpService:JSONEncode.
Buffers are compressed before encoding, so you might be able to fit more, but be careful as different data will have different compression ratio.