I think the best utilitarian camera out there other than the 1DX is the Canon 5D MKIII. IMO, in real world practice, it only lacks the FPS of the 1DX. Having a dedicated processor is nice on the AE on the 1DX. But unless you are thinking of going full time pro, I don't the think the 1DX is really necessary. The 1DX is really good long-term investment though.
Except for the Sigma 50, I say sell your other lenses and get a good 24-70mm f2.8 and 70-200mm f2.8. With a great set of these, you can do just about any kind of photography with them. Unless you are positive you want to go prime lens. But you already have the Sigma 50 and that can be used for lots of things.
I just rented the Sigma 24-70mm f/2.8 IF EX DG HSM and thought it was spectacular. It's almost as sharp as my Zeiss 50mm f1.4 and the bokeh might be better. You can go used/new for $800/$900. The only problem I have with it is that it's not weather sealed. But the Canon 24-70L is 2.5x more. Unless you can get the older version which is supposed to be almost as good. And less than half the price used. If you can find one for sale
Those puppies are gold.
I'm sure you know how awesome the Canon 70-200's are.
People use those for sports, portraits, weddings. Lots. The MKII version is so bad-ass and an excellent long-term investment. If you can get one on sale, it's not hugely more expensive than the MKI version.
So at sale prices and money from the sale of those two lenses, that should give you a few hundred dollars left. Maybe buy a Phottix Mitros+ flash gun? Hopefully you have a sufficient camera bag. Maybe 'borrow' one of your school lenses for a backup