You should be able to cluster the channels on less connections
or rearchitecture to reduce the connection count.
Consider perhaps, creating a send and a recieve bot.
Since you don’t need a connection to be in a channel to send a message your send bot doesn’t even need to be in the channel. So doesn’t have to worry about code to handle incoming messages.
And you can cluster many small channels on a single connection. Due to low chat traffic.
I don’t think being verified will help you with your connection issue.
So you just want to group together chats onto less connections