Query: Trying to host a site for free on custom subdomain but facing issue

I'm trying to connect my subdomain eminom.run.place to my Vercel project, but I'm stuck on a domain ownership verification issue. My website is already deployed and working on its vercel.app URL. I got eminom.run.place through FreeDomain.one. I can manage the DNS records for my assigned subdomain through their dashboard. But when I add eminom.run.place to Vercel, it says the domain is already associated with another Vercel account and asks me to verify ownership. Vercel requires this TXT record at _vercel.run.place I contacted FreeDomain.one support, and they confirmed that the parent domain run.place is managed by a different account. They cannot add the TXT record because I don't control that account. I only have access to my assigned subdomain. My questions: Is there any legitimate way to verify eminom.run.place ownership without access to the parent domain's DNS zone? Is there an alternative way to use this subdomain with Vercel, or should I request a different subdomain? Are there any free domain or subdomain providers that work reliably with Vercel and allow users to manage their own DNS records? I don't want to have the vercel.app domain and I'm trying to get a domain which has my tag on it but not the money to buy that.