I'm not sure there's a way to do what you hope to.
Embedded data is specific to the individual response, so even though you can use it to add up the number of registrations within one response, you can't add the values from one response to previous ones to get a net total. (Same with using scoring methods.)
Quotas are based on the submission of the response. So one response, even if it has 15 registrations counted within them, is still just one response against the quota. Also, Quotas only come into play at the time of the submission of the response. So it is possible you'd have seven people all submitting 10 registrations, and if they were all filling in simultaneously (eg all started before the quota was reached), they'd still all be able to submit the form.
This support page feels relevant, and may help: https://www.qualtrics.com/support/survey-platform/common-use-cases-rc/appointment-event-registration-surveys/
I suspect you would need each registration to occur via a single submission of the form, in order to use Quotas to manage (and at least minimize how much overage due to simultaneous submission can occur). .... Of course that adds up in completes.