Kolab Now https://kolabnow.com/ - This is run by Kolab who actually employs several of the Roundcube developers. You shouldn't have any problems with outdated Roundcube on this service.
Hover https://www.hover.com/email - Owned by Tucows (one of the oldest companies online) they have supported Roundcube development and are active on the mailing lists. They do seem to have a custom skin on Roundcube, I'm not sure how different it is but Roundcube is definitely underneath.
I haven't used either but either one will work better then your current service.