Why not " Nui nā woela o kēia huaʻōlelo. "
That would translate more to "There are a lot of vowels of this word." I think this sounds awkward in both English and in ʻŌlelo Hawaiʻi. It would probably still be understood, but not natural.
Aloha e ke hoa. Take a look at your Na Kai 'Ewalu (2012) puke 1 'ao'ao 192. Nui ke one o keia wahi. = This place has a lot of sand.
ʻAe, e kala mai. I think after reading the DL answer, I could not change my brain to make sense of your suggestion. Reading it now, it makes sense completely. Mahalo nui i kou ʻike.