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There isn't any alternative, NS doesn't allow non-admin roles to edit admins, you could potentially set giveAccess = false to all the admins, congrats, now you don't have an admin

perhaps a carefully crafted Suitelet-as-API that is set to run as Administrator role?

try it? I don't think so, I don't think you can edit employees with the admin role unless you're an admin and in the UI