You could probably disconnect the brake input wire to the Autopage. As far as I recall, that wire is a security feature that is intended to prevent someone from being able to break a window, crawl in to your car, break the steering lock, and drive it away since most cars these days have a shift interlock activated by stepping on the brake pedal. I'm not thinking of any reason on a push button start vehicle that does not require putting a key in a key cylinder that you would need the brake pedal input connected.... Maybe someone can correct me if that's not the case. I've installed a few remote start systems and don't recall any other reason for that feature.
If you opt to try disconnecting the brake pedal input, before tying the wire up and buttoning the trim panels, etc. back up, do a test. Start the car, confirm pressing the brake pedal does not **** the engine, then use the push button start switch to try to shut the engine off. If the engine does not stall, then you may need to live with the brake pedal **** feature.
Another test before you call the modification good would be to take the car for a spin around the block, get back to your house, put the car in park, but leave it running. Leave the engine running for at least as long as the remote start cycle lasts (programmable, usually something like 20 minutes is the default). Without the brake pedal input, the remote start system may never **** the timer and therefore the remote start system might stall the engine when the timer expires, even if you happen to be in the middle of an intersection when that expiration happens.
-Rod