How to search and replace globally, starting from the cursor position and wrapping around the end of file, in a single command invocation in Vim?

You are already using a range, %, which is short hand for 1,$ meaning the entire file. To go from the current line to the end you use .,$. The period means current line and $ means the last line. So the command would be:

:.,$s/\vBEFORE/AFTER/gc

But the . or current line can be assumed therefore can be removed:

:,$s/\vBEFORE/AFTER/gc

For more help see

:h range