The words headlong and headfirst were, I think, at one time, quite distinct, but in typical sloppy American usage, the distinction between them has blurred, as do all subtle distinctions, when subjected to mindless and uncorrected use. (Heh, heh, heh.)

Headlong carries/carried two senses: one was fast and the other was rash. The first had to do with speed, often excessive speed, and sometimes carried a whiff of negative judgement (as in "too fast") in its usage. The second had to do with the lack of adequate consideration before an action and this, also, carried with it a just a hint of negative judgement (as in "poorly considered") in its usage.

Headfirst was/is used entirely posturally, I think. One dives headfirst into the pool. The car plunges headfirst off the cliff. If this is correct, then a thing without a head (literally or figuratively) cannot do anything headfirst.

I have no authority whatsoever for any of these assertions and am going to take my lady love to the movies rather than spend time looking any up.