I have edited the .htaccess file trying various redirect rules in order to point to the new static index.html page. To no avail, it still ends up showing the old Wordpress version. This seems like a very straightforward edit, but I've been hitting my head agains the wall. I can share the rules if needed. Would love to get any assistance and thanks in advance.
I would NEVER recommend having a temp home page while you work on the live site. You'd be much better off to keep the current site live, and build the new version in a temporary location -- either a new WP installation in a sub-directory, or... BETTER YET: get a new Managed WordPress package, build it there using the provided temporary domain name. Then, when you're happy with the new one, you just change the domain name to point to the new version. I have done this process many, many times, it is much better in the long run.
There are some good reasons not to hide the current site, and replace it with a one-page temporary site. For starters, people will be annoyed that there is not much info if/when they find you. Unless there is factually incorrect info on the old site, I'd leave it as is.
When I take on redesign projects, I NEVER put a temp home page up (unless there is not even a site to begin with, in which case it's a new site and not a redesign). There is no added value or benefit in doing so, and it makes you look bad. Better to work on the new version in stealth mode, and just replace it when it's time.