Can I route using the leftmost portion of hostname with a wildcard for everything after?

Solution 1:

If I understand your concept correctly, then this won't work.
You can have multiple subdomains in a single rule, but you can't have something like api.*.example.com or api.*.com

Number of rules doesn't matter in this case, you will get this error:
Asterisk may only be used as leftmost character preceding '.' or '-'

So you'd have to add every subdomain separately.