I'm looking to do ceiling inspections, need a drone that has a camera that points straight up (or, at least 45 degrees up).  Has anyone come across something like this?

Going to need one for indoors.  How close do you have to get to ceilings and walls?

I would think you are going to need a drone built specially for the job. A Phantom is just going to be looking up through the props.

I found a couple on the web, searched for “flying camera platform” rather than “drone”. Most seem to be expensive professional film makers equipment. You may have to mod one yourself or find someone who can.

It's not cheap but DJI's Matrice 200 can be fitted with an upward gimbal specially for inspections .
https://www.dji.com/matrice-200-series

The Phantom series is not adequate for your ceiling inspections,  agree with Labroides, you may need a special drone, like an M210, but it is not cheap.

Before I spent buku money on a specialized drone I think I'd try a low-tech solution like a mirror in front of the camera.  Yeah, you'll be looking up through the props, but this isn't exactly cinema work.

If that's too kludgy, you could always build yourself a drone that has two cameras mounted on the frame.  Use the forward facing FPV cam to fly up to the ceiling, then flip to the other frequency (top cam) and carry out your inspection.  As long as the drone isn't wobbling all over the place I don't see why you'd need a full gimbal.  Tilt would be nice.

GoPro makes a gazillion different mounts for its cameras and it would be a simple task to just slap one on to the top of a Phantom (or any other quad for that matter) and it would point straight up.  Sure, it might interfere with the GPS module, but hey, it would be flying indoors anyway where you couldn't get any reception.

Such a pity we can’t fly upside down, would a gopro fit on top of a phantom. I can’t visualise in my head how much clearance there is and I don’t have my drone handy.
Edit
I didn’t see the post above mine already mentioning a gopro

You'll need a Karma for that !!!!!!!!

A GoPro mounted solidly on top of a Phantom seems sensible, you can use the wifi to see what you are doing and take photos unless your ceilings are really high.  It will need a solid mount or there will be too much vibration.  The Phantom is a good choice of drone due to the visual hold, much easier to fly indoors than most, if there is a decent amount of light.

Also put some sort of tall spike on top so that the props can't get too close to the ceilings, the airflow into the props will get uncontrollable as the props get close!

Might be better to use one of the 90 degree action cameras so that you don't have to get so close, eg a Gitup Git2P90.

They dont like gopro's sat over the gps

Aerial-Image Posted at 2017-10-20 09:41
They dont like gopro's sat over the gps

Good, you don't want the GPS working when you have a ceiling anyway!

The Mavic Pro has an option to tilt up 30 degrees, not sure if that would be good enough.

Maybe add a small action cam on the back of your Phantom?
Not adviced by DJI probably, but it might work (as long as you have enough clearance with the props)

I fly indoors for video shoots all the time.  You don't need compass or gps.   All you need is prop guards, practice, and balls.   A small GoPro like the Hero 4 Session  on top of the Phantom would work fine.  You can be creative with a home made mount to diminish vibration, and use industrial grade velcro to mount it.   

DJI has one but is way too expensive around USD$12,000. There is; however, an option for you. I found what you need. Hope is not that expensive for you, you can buy it from Amazon or Best Buy for USD $700. The drone is from Parrot and the model is ANAFI. Here is the link: https://www.parrot.com/us/#anytime-anywhere  Let me know how it goes...