Subdomain-based multisite, but giving wordpress its own directory?

I have created a wordpress site at Knowing that in the future we'll have a few branches that do similar things in different regions of the country, and I'd like to have to only purchase themes/plugins once for all the regional branch sites, I thought that choosing Wordpress Multisite would be the best way to go. And I chose to install wordpress in its own directory (/wp/), as that seemed to be a general best practice, which I'd used before for single site installations. Also I wanted to be able to develop it and get feedback from others while the old site was live, so hiding it in a /wp/ was great. However, now the site is live and I'd like to eliminate the /wp/ from the url. Also, I'd like it to use www, though I initially set it up without www. Later, I found out that wordpress multisite best functions when it's in the root directory for the main page. Oh well.

Currently, if someone goes to it redirects to
But if someone goes to it does not take them to (which is where they get to if they click on the 'Registration' menu link from the home page).
Instead, they are redirected to
Which is a page that includes the homepage slider, and "The site you were looking for,, does not exist."

So I can see that there's some redirect loop happening.

Things I tried
I tried following the instructions here:
Which I combined it with the following htaccess:

RewriteEngine On
RewriteCond %{HTTP_HOST} ^ [NC]
RewriteRule ^(.*)$$1 [L,R=301]

RewriteEngine On
RewriteBase /wp/
RewriteRule ^index\.php$ - [L]

# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(wp-(content|admin|includes).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(.*\.php)$ $2 [L]
RewriteRule . index.php [L]

The results of that combination were that people would be redirected to the right place (.com/registration redirected to .com/wp/registration), but going to wp-admin (or wp/wp-admin) would result in a 404 error, thus preventing me from being able to edit the site.

I have also tried using the 'Change website domain' tool in the cpanel wordpress toolkit, which didn't work, though I was able to successfully use the 'staging' tool in the cpanel wordpress section to successfully create a functioning staging subdomain (but only after all this mess.)

Currently, my htaccess has the following in it:

RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]

# add a trailing slash to /wp-admin
RewriteRule ^wp-admin$ wp-admin/ [R=301,L]

RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule ^(wp-(content|admin|includes).*) $1 [L]
RewriteRule ^(.*\.php)$ $1 [L]
RewriteRule . index.php [L]

and my wp-config.php has these lines of code:

/* Multisite */
define( 'WP_ALLOW_MULTISITE', true );
define('MULTISITE', true);
define('SUBDOMAIN_INSTALL', true);
define('DOMAIN_CURRENT_SITE', '');
define('PATH_CURRENT_SITE', '/wp/');
define('SITE_ID_CURRENT_SITE', 1);
define('BLOG_ID_CURRENT_SITE', 1);

Which I tried messing with when I tried eliminating the /wp/ and forcing the www.

The index.php file in the root directory has this line:

/** Loads the WordPress Environment and Template */
require( dirname( __FILE__ ) . '/wp/wp-blog-header.php' )

Which I also tried modifying to eliminate the /wp/

I've also tried moving all the files out of the /wp/ directory, and removing /wp from all areas that I could find it (including the wp_sitemeta wp_site wp_options and wp_blogs tables in php_myadmin, but not doing an exhaustive database search/replace). That didn't work at all, just 404's and 403s abounding.

So far nothing has given me the solution I'm looking for (ideally, having multisite functionality, but not having /wp/ in the path name. At this point I don't care if wordpress is in its own directory, or in the root, as I've moved the previous joomla site away, so I won't be breaking its index.php or cgi-bin directory, etc. Should I just do a fresh install of wordpress and export/import the data?

Thanks in advance.