Yes, I guess MightySites can help here. You will have a main site with usual hosting account, all clients sites will be parked domains with own databases. So one Joomla installation for all sites will be used. You want "it would automatically flow out ...

Gantry framework and most RT extensions don't have own database tables, so they don't require additional support and work as usual.

... has their own log in to access their sub domain on site.com. - Not any other sites or the master account. Each of your subsites will have a usual Joomla backend like http://cust1.site.com/administrator, each site can have own users as usual. So user of site A will have access to site A only ...

... subsite.mainsite.com, so all sites will use same Joomla installation and share files (including images). Subsites will have own database data as usual, but load JReviews, Users and all JomSocial data will be loaded from main site. So JReviews, Users and all JomSocial data will be always same ...

... if "siteB.com" is parked on top of "siteA.com". Is that correct? Rick Yes, correct. Parked domain is visible to end user like usual domain with own hosting account. User can't even know if the domain is usual or parked.

You can either share templates and their settings, or each site will have own (separate) templates and styles as usual (except YooTheme templates because they store settings in files and sites which use same Joomla installation will have same template settings).

Bridge can copy phpBB users to Joomla.

phpBB ACP runs as usual, it is not wrapped in Joomla administration.

MightySites can clone database table set from one site for new site.
Each can either have own classifieds (as usual) or share classifieds with other site (so both sites will always have same classifieds).

... guess that this would be / could be supported by MightySites? What do you mean as "supported"? All extensions work with MightySites as usual and there is no need for additional support. Additional support is required only if you want to share extension's data across sites. For this ...

It can be used as usual if you don't need to share its data across sites.
In case of sharing support please create a ticket in our Support Center and attach this extension, we will add a support for it.