I'll suggest 'to kowtow'. The noun sense is
The Chinese custom of touching the ground with the forehead in the act of prostrating oneself, as an expression of extreme respect, submission, or worship.
[From "kow-tow | kotow, n.". OED Online. September 2015. Oxford University Press. http://www.oed.com/view/Entry/104417 (accessed October 23, 2015).]
But the verb probably works better in your example sentence:
a. intr. To perform the kow-tow. Also transf.
[From "kow-tow | kotow, v.". OED Online. September 2015. Oxford University Press. http://www.oed.com/view/Entry/104418 (accessed October 23, 2015).]
So,
They all fell to the ground, kowtowing.
If, however, you want to use the noun 'kowtow', this works:
They all fell to the ground, performing the kowtow.
Whether either form will work depends on the context. Use of this borrowing from Chinese may be uncomfortable in some contexts.