Long Power Cord

Romex.

Seems like you would be better off having a new outlet installed. If access isn't too much of a problem it would probably be less expensive than buying a quality 25ft power cord

You could also consider a combination of the initial thought and the suggestion above.

Buy some quality bulk wire and run it to an outlet near the projector. There are numerous conditioned/protected outlets now available from PS Audio and MIT which will condition the power for your projector should you elect to add a dedicated line.

Feel free to contract me if you need help with the project.

That is one heck of a LONGGG ass.

As thick as possible. Long extention cords can cause a voltage drop if the wire gauge is too small. 12 gauge or larger should be fine.

If you can run Romex inside the wall from the power conditioner to the projector it would be ideal. Just terminate it with good quality connectors.