Another way is to go weird, and do
where $m$ is the message that is pre-encrypted with a OTP. This is a good example of code book mode working properly, due to the OPT. No cuddly polar creatures appear, and it follows the recommended encrypt then MAC doctrine.
$nonce$ is my message order(and pad ID for decryption), but it's not sequential. It's difficult in practice to maintain a correct (non repeating) sequence. It would be truly random, drawing upon the OTP key material. If you have the resources to make Kolmogorov random key material, then use it. Don't forget that if you also need a temporal component for the order, you can just introduce a timestamp into the message plain text.
I like this approach as it's simple to understand and implement. Java would only use existing internal functions as AES and SHA* are inbuilt. You just choose the bit length of the key, hash type and nonce. So you could have 256 bits throughout for symmetry. I think that I'd make the message length an exact multiple of 128 bits, for no particular scientific reason other than feng shui.
Using a separate key for encryption of the OTP key material has another advantage. It creates an ersatz two factor encryption system. Even if the OPT falls into enemy hands (say by just seizing the PC), past messages cannot be read.
It's worth pointing out that this is an atypical use case, and so I can't find loads of authenticated OTP research material. This leaves unanswered the question of whether you should include the OTP ID ( my $nonce$) within the MAC. You could I guess in minimising lookups for corresponding pads.