Hi Lamberto, The answer really is to get some new bindings. Your old bindings don't owe you anything, and you'll be playing with fire if you try to extend their service. With the money you have saved by riding the same old bindings and boots (and presumably board) for so many years, you can treat yourself to new bindings. What is more expensive, new hardware on your board, or new hardware in your ankle or leg?
Intec-style step-ins work great, I've been using them for 10 years. Just visually inspect that both pins are engaged and off you go. Certain snow/air temperatures can cause a problem with snow sticking to the soles of your boots, but I think the convenience the rest of the time outweighs this. Just scrape your sole on the heel receiver. But this is probably a moot point as you don't want to upgrade your boots, and that's fine if they're really working for you.
It is not true what you say about the old Burton "rat trap" bindings. There is a way out of any over-center cam device like that. It can happen during a hard impact to the bottom of the board, like during very heavy chatter or landing a jump flat, and especially if the the bindings are sized too loose or too tight. Step-ins, on the other hand, if properly clicked in, are much more secure. It would take a much more catastrophic event to release your boot from step-ins.
EDIT - unless by "rat trap" you mean the old Burton step-ins that slammed closed like an actual rat trap. I'm not too familiar with those, aside from painfully getting my finger caught in one at a snowboard shop once.