Is it possible to register an LLC while abroad so that I can keep on working as a contractor through the new company until I return to the country?

Why would you get better hourly rates through an LLC? The LLC changes absolutely nothing about your tax situation, it is completely 100% disregarded, as if it doesn’t exist at all.

Anyway, LLCs are a state thing. Check with your state (which is unknown here) to see what they permit.