However, the door has opened into the metal rod that sticks down from the rail.
The rod you're referring to, is that the same as piece that's hitting your door in the picture? If so, that's called a drawbar - specifically an adjustable J bar is what you have. You seem to have a really long one for some reason, which is unnecessary given you have low headroom. You can shorten that up significantly by purchasing a shorter one to get a couple more inches.
Garage Door Opener Operator Arms
While installing pipe insulation is a great idea and something I will be doing, something that still worries me is that the door opening into the pipe-insulated metal rod that sticks down can still put unnecessary pressure on the garage door track itself and risks damaging the rail/mechanism/garage-door.
I can't tell if you have a chain or belt drive, but either way that rail is pretty sturdy and doesn't typically take on much damage. If it's a commercial installed opener it would be a 1 piece bar and a 2 piece for a DIY opener, and that does allow another wear point. What could also happen is that bolts around the draw bar or going into your door would wear and open up.
We had a similar problem a while back in one of our garage bays, and actually ended up scraping the rear liftgate of our minivan with the drawbar. I decided to rip the entire opener out and installed a Liftmaster 3900 Jackshaft opener. This eliminated that center bar altogether and gave me a bunch more clearance.
The picture below gives you a good view of the differences. You dont have to have a high lift to do this; your opener would just sit to the side instead of having a center bar.
Has anyone placed a FWD sensor-opaque object at the height of the rail so the door more reliably detects the rail?
The right bay on the picture above could also solve part of your problem, but you don't have too much room up there.
I wonder how much the contractor gonna charge for such conversion
Depends on your area. As low as $500, as high as $2000. I did mine myself, it wasn't too difficult of a conversion; but I have installed doors and openers on my own before. Most that quote above $1000 USD includes the opener which runs $200-$300 by itself.