Might be a case for a custom build
Try flying in this environment before you put a lot of effort into it.
Apart from gimbal or mounting difficulty some potential issues to consider:
Losing GPS under bridge decks
Possible magnetic interference if you are close to a lot of steel.
Have you tried the gimbal adjustment that lets you point the camera 30° above its normal horizontal position? I realize that it's nowhere near the upward viewpoint that you're looking for, though. And one of the drawbacks is that the props sometimes get in the picture.
Ran into a friend yesterday who was telling me how his aerial inspection business was really taking off (no pun intended). He is using a drone with a camera mounted on the very front so it can tilt up as well as down - unfortunately I can't remember the drone maker. He did tell me they were buying a Lockheed Martin Indago quadcopter with a 50 minute flight time. Not sure if it has a front mounted camera though.
Be aware that you lose satellite under the bridge. Also if very close the rebar does throw off the compass.
The winds seem to funnel under some bridges as well.
You can try tilting the P3P camera up slightly and fly backwards. Use the bottom 2/3 of the frame for report photos.
Albris, a quadcopter from SenseFly, has a camera (visual and thermal) with the ability to turn from 90 degrees up to 90 down. It Includes collision sensors all around and the ability to program and set their trigger distances. It aims at professional flights, but including Pix4D software bundle, 13 thousand Euro (in Spain) seem not crazy