Horticulturist or Horticulturalist
Chris Fox in the School of Languages and Cultures has passed your request on to me. I have been broadcasting on language for the ABC for nearly 20 years, and do a column on language in the Courier-Mail on Saturdays, and I have major research interest in English in Australia.
The Oxford English dictionary does not even recognise "horticulturalist". It lists only four words ending in -culturalist: culturalist, agriculturalist, multiculturalist and permaculturalist. And of these agriculturalist and permaculturalist have alternative forms: agriculturist and permaculturist. There are in all 12 ending in -culturist, like pisciculturist.
So your preference for horticulturist is correct. Another practical way to check is on Google, where horticulturist has about 10 million hits, while horticulturalist (which, by the way, actually is recognised by my spelling checker) has only 687,000.