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

Hello,
I have created a wordpress site at http://www.renaissanceadventures.com. 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 http://www.renaissanceadventures.com/ it redirects to http://renaissanceadventures.com/wp/
But if someone goes to http://renaissanceadventures.com/registration it does not take them to http://renaissanceadventures.com/wp/registration/ (which is where they get to if they click on the 'Registration' menu link from the home page).
Instead, they are redirected to http://renaissanceadventures.com/wp/wp-signup.php?new=renaissanceadventures.com
Which is a page that includes the homepage slider, and "The site you were looking for, http://renaissanceadventurescom.renaissanceadventures.com/wp/, does not exist."

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

Things I tried
I tried following the instructions here:
https://premium.wpmudev.org/forums/topic/how-to-change-url-for-wp-multi-site
Which I combined it with the following htaccess:

RewriteEngine On
RewriteCond %{HTTP_HOST} ^www.renaissanceadventures.com [NC]
RewriteRule ^(.*)$ http://renaissanceadventures.com/$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', 'renaissanceadventures.com');
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.