Is there a casual alternative for よろしく. For example, when speaking with close friends, I want to say something along the lines of "from now onwards, lets continue getting along", or something along those lines. The best I can think of is これからよろしく but that sounds extremely stiff and formal
よろしく is already fairly casual and colloquial, and you should not seek even more casual alternatives. In formal situations, you must say at least よろしくお願いします. You should say どうぞよろしくお願い致します when you need to be very polite.
(Well, there are よろ and シクヨロ, which are much more slangy and charai, but I'd say "don't use them", especially as a equivalent of "nice to meet you". If you used them, it might sound just funny because you're a learner, but if I used them I would probably sound over-friendly and even offending.)