Viewing distance is incredibly important. It's incorrect to assume that all images for printing need to be 300DPI. If you find out the line screen of the final printing process, that will give you a hint to the maximum DPI needed for great reproduction.
Info about line screens of printing halftone patterns on Wikipedia
Why so big?
What's the use case for the 30.5 × 10.36m print? Is it a for a conference wall, where people will be walking right alongside it? If so, you'll need to do what you can to get the image looking great. Is it a billboard or poster than will be several meters away from the viewer? If so, pixelation may not be as much of an issue — a long time ago I created a billboard image with a (professional) 5MP camera. Pixels matter, but sometimes quality of the source is more important.
The best way to test all this is to create a sample portion of the poster at the right size, get it printed using a similar technique and see for yourself if it's acceptable or not. You can sell it into your boss as a potential cost saving, because large format prints are expensive, so mistakes with large format printing are a bad idea. You really only want to print the final poster once.
I've worked on lots of billboard advertising, but I don't think I've ever needed a 86400×29376 pixel file. That's pretty big!
Talk to your printer
Your printer should be able to point you in the right direction. I'd suspect you don't need to target such a high DPI though. In fact, it's typical for large format projects to be set up and 1/2, 1/4 or 1/10th scale in InDesign (or the app of your choice). So your printer might advise 150DPI at 1/4 size, or similar.
Techniques for scaling
If you do have to scale the image, I'd recommend using nearest neighbour and scaling to an exact multiple (200% or 300% etc). Or, try the other different scaling methods and see which you like the look of the most for the image you're using. Once you've done that you can add a little bit of noise (which will be done at the new resolution) and/or blur specific portions of the image, keeping complete control over how each area looks. This is what I did with the 5MP billboard image I mentioned earlier.
Don't trust any app that says it can magically add detail to an image. They can't. Try as hard as you can to ensure the source images are as high quality as possible. If the boss's sister's boyfriend took the photo on their iPhone, gently and calmly request that the photo be retaken with a better camera and/or by someone who knows what they're doing.