The goal isn't to make the networks seem like one and connect resources across accounts, which is what those products do.
My goal is to access private resources via SSH bastion/jump machines in a specific account. There's a few ways to do this in AWS, but all of them are more costly by a pretty wide margin.
You can forward ssh through ssm, and dump that into your ssh config file. Works pretty nicely with some of the sso automation for the cli that's around these days.
Without knowing the specifics of your situation, I would slightly suspect client/configuration if you’re encountering encoding issues. In my experience, integrating ssh and ssm is quite stable (provided you’re using OpenSSH and not a specific language client’s own implementation of the protocol).