Hi there! To start off with, for accurate information you'll want to contact sales and support at Red Hat directly, this is mainly a discussion forum. As a starting point, you'll want to visit https://www.redhat.com/en/contact and https://access.redhat.com/support for links to more information about how to contact Red Hat and for support policies, if you don't have a contact already.
The RHEL support life cycle is discussed in detail at https://access.redhat.com/support/policy/updates/errata/. You're correct that RHEL 6.10 is the last minor release of RHEL 6, and RHEL 6 will exit Maintenance Phase 2 on November 30, 2020. To extend support and access to whatever new errata Red Hat still provides beyond that time, you will need to have an Extended Life-cycle Support (ELS) subscription for that server.
Your best bet is to talk through this with your sales or support contact and figure out what the best approach to this will be for you...among other things, Red Hat will want to make sure that ELS is a good fit for your use case so that you have a positive outcome. It's actually in Red Hat's interest to make sure that you have the solid understanding of the add-on that you're looking for (Red Hat would rather have you happy with your experience with ELS, and keep you as a happy customer when you're able to upgrade to a newer version of RHEL.)
