The hypothesis isn't supported by the fact that the dynamic server's busting its balls. If long-running queries were causing threads to stall leading to too few threads being available to service connection requests, one would expect the dynamic server to be waiting for the busy database server to complete those long-running queries. But there is no busy database server ...
If it were me, I'd concentrate on that Tcl server and not worry about anything else until I had a reasonable understanding as to why it is so heavily loaded.
