Except for the Solaris, the other's would drop the rate some. There's just an abundance of people with that experience set. But the on-call would bump it up...
Sounds almost as if it's a sideline type of thing. In which case, it's changes the rules too. You'd need to figure out what the impact of taking it on is (how would it affect your being able to do other things since you could be at their beck and call), what they'd be willing to pay, and what you'd be willing to accept.
The higher rates being thrown around are more for contract positions (ie 8hr/day) or even contract to hire positions. When I was doing per call type of work (which was way back when), it was much more than you were getting from these people in the past.
If you've got real skills (ie troubleshooting, kernel tuning, etc.), you are almost definitely selling yourself short. The problem is now you've set a precedence, or does the new guy not know what you got previously? They might object to you trying to jump the rate up on them. Have a good argument for it if you do (ie. this is what I'd need to be able to ensure that abc co. continues to get my priority attention to matters). That could potentially give you another way to go if they balk. Well I could continue to do it for $x/hr but realize that my other contracts would have to take priority. BTW, very few customers no matter how little you charge will understand that customers paying more will get first dibs on your time. They will want it fixed, and quick.