Hi Carla,
Thanks for stopping by and asking a question. While there are many great websites that implemented parallax scrolling, only few of them were able to strike a balance between both, SEO and UX. Please accept my sincere apology for not being able to name them here for many obvious reasons. However, let me tell you few things about your project at hand. If your website is not in to creative niches like, design (can be website design also), art, e-commerce (catalogue websites), studio etc..
1. you should be giving more emphasis to the quality of the content and its size on the homepage especially if you want to rank for any keyword /phrase using with your homepage.
2. Good content of about 600 words should be great with a keyword density of around 1% (this is excluding the keyword presence in other indexable content on the page like the meta information, heading tags, image alt text, image titles).
3. Good code to text ratio, though this is not a hard and fast rule. Personally, I like it to be around 25%.
4. Sizeable content in the first fold and this does not mean to dump all your content in the first fold.
5. Other on-page SEO factors.
If you are into the creative niche, you can lean a bit more towards the UX side.
Hope the above help and again please accept my apology if my response has not lived up to your expectation.
I wish you all the very best for your up-coming project.
Best regards,
Devanur Rafi.