Earlier quoted context omitted.
Maybe try InputStick then? Though I think 100 random characters is well beyond the point where you're no longer significantly increasing security by adding more characters. You can easily get 130+ bits of entropy with only 20 characters, and even for a ridiculously weak hashing algorithm like MD4 that'd be enough to withstand the entire combined strength of the Bitcoin mining network attacking your password for well…
This is the solution I've come up with as well. It's saved a lot of frustration already, which builds up quickly with when you have to retype even a 16 - 20 character random password over and over again in a short period of time. I only wish for a better iOS experience and direct integration with 1Password. Oh, and a way to prevent random connections from having keyboard access if I were to forget to unplug.
Pretty sure that already exists, at least on Android. InputStick lets you set up a pre-shared AES Key and pairing PIN that you need in order to connect to the device.