Not really. SOHO class routers aren't big on processing power, and aren't made for fast reboot times. They're also not meant for tinkering so it's difficult to script or access them with tools for management.
If you wanted you could try replacing your setup with a computer running Linux, or one of the Linux projects that will flash your router with a new OS and it might be faster and more functional.
You seem to have two issues here but don't state why the requirement is such; you wanted to know if you can remotely restart the router, which you can with the web interface or a power product that you plug into your power outlet and then plug the router into that then remotely flick power on and off to the router. So yes, you can get it to reinitialize. (Alternatively you can find an application that will script the procedure for restarting from a computer on your network.)
Then you mentioned it takes 30+ seconds to restart it. Is there a reason you need it up ASAP, or just impatience? Even our Cisco routers can take a couple minutes to come back up if power is cycled on them. Most routers aren't meant to restart so it's not a common occurrence, in turn boot time isn't a priority or feature to manufacturers.
EDIT:I'll also add that even if you script it or find another way to do the reboot, the more complexity you add to the "system" the greater the chance you'll be increasing headaches down the road. Technology tasks should be as simple as possible before the odds of failure tip the scale into being a pain, and doing something like coming up with a script on a computer to attempt a reboot of the router only increases the chances that something will go wrong.
If you absolutely need to keep it up all the time without changing addresses, you might want to contact your provider about getting a static IP. Depends on what your situation is and how important these headaches are for you to avoid.