I took the liberty to modify the script a little in regard to tray icon display and a (fake) tray tooltip. It is an older build based on v1.7.9.1 and is only a proof of concept. It does feature a few code fixes aimed at x64 compatibility but there's still a lot of work to be done to achieve that goal. There are also a few bugs related to the fake tooltip positioning and timing, at startup and while changing options.
@ Ath: That's why I mentioned me using the QtWeb 3.8.5 browser. My hardware is quite old and limited, the OS is XP-SP3, therefore I prefer this very lightweight browser.