OT - Ports and changing them

[Aiken]

I'm not an expert, but you can try to redirect your connections to the socks proxy. There are some utilities which allow you to force many programs to work through socks proxy, such as SocksChain or FreeCap.
They'll open only 1 port for all connections (10xx, usually), so it can solve your port problems. Maybe.
Downside of this is that you'll have to find good, stable and free socks4 or socks5 proxy. And they're quite rare.