Aww Matko, that sounds super infuriating! We've been missing you too! If Mat's fix doesn't help, try posting what you've posted here in the 'Community Led Technical Support' forum on the Runescape forums, here:
http://services.runescape.com/m=forum/forums.ws?409,410It's where the clever techie types like to hang out to demonstrate their clever techiness by solving people's technical game play issues. There's probably someone there who will have some more ideas of what to try.
In the meantime, enjoy relaxing and having some 'you' time! You've certainly earned it! Hope to see you back in game again without all those issues soon!
Edit: I've just remembered something a Jmod told me recently (not a techie Jmod) when I was moaning about the nxt client being super laggy for me. He said to leave my account logged into the lobby for a couple of hours before playing. I've no idea what difference that might make, or if it would help in your situation, and I dismissed it as being rather impractical. It might be worth a try though if you're desperate.
I've also found that the old client is less laggy by far for me, so when I'm not on two accounts at the same time (when I have one account on each), I play on the old client.