Well let’s talk basics first!
You can’t divorce SP from the base WP it is held within. SP needs the Wp users and usermeta tables. So basically you arw talking about most of the WP database.
If this were me I would merge the two forums on the source site to get them down to one and then backup that site’s database. When you restore to the new site you can then rename that forum to the one you want.
However – due to the domain name change you will have to recreate some of the forum options. Anything with a URL will point to the old address and because of the way some data is stored it will trash some of the option records so going through al of the admin panels and checking it all is going to be required. Not a long job but a necessary one.
Any in-site urls in forum posts will, of course, point to the old site.
You will also need to visit the forum admin > toolbox > housekeeping and reset the profile tabs and menus beofre profiles can become usable.