Does the fervent hopeful belief mean that you think he already reached the status of Chezkas Moshiach?
Don’t whitewash it. For the meshichists, it’s more than fervent hopefulness, it is a clear belief.
It’s even more than chezkas moshiach, they hold he’s vaday moshiach.
I’m sorry if you think a source is needed that it’s not okay to make up your own Rambam.