First off, you don't need mobile network coverage for your phone to work indoors - WiFi-calling is available as a mitigation for any indoor coverage issues whenever and whyever they occur. As has been pointed out, no network guarantees indoor coverage or even service in any specific location - despite the best efforts of coverage mapping.
If the outstanding amount in question had been recorded as a default on your credit file (your reference to external DCA suggests so), and you then subsequently paid it, then to mark it as settled is entirely correct process. Not just for EE, but the credit reference agencies & wider financial services industry.
Ombudsman decisions are binding on the organisation if you've accepted the outcome, but are otherwise free for you to accept or reject. If you're not happy with the outcome, your next step would probably be to consider a civil action - most likely in the small claims court - for any financial loss you have suffered due to what you presumably allege is a breach of contract. I would strongly recommend you seek independent legal advice before proceeding here, as I wouldn't be too surprised if the Ombudsman decision would be persuasive.
Certainly, it's quite common that if an unresolved complaint has already been referred to external arbitration, the "higher ups" as you put it, won't add anything further to what may have already been said.
