If you want them to mean something, you need to have a direct connection with the carrier of your user, and you have to know that the carrier or their network doesn't just fake positive delivery receipts at some point in the system to make numbers look good. With an aggregator between you and the carrier, you have no way of knowing when the delivery path changed and the intermediary faked a delivery report.
The absence of a positive delivery receipt doesn't really mean anything either. Negative delivery reports have some information content though.
My context is sending verification codes though; receiving a code back from a user is a much better measure of successful delivery to the user than a delivery receipt. If you're sending news or something where there's no measurable direct action taken as a result of the message, I guess a delivery receipt is better than nothing, maybe?
Realtime measurement and thompson sampling or multi-armed bandit with as many credible providers as you can manage is the best way forward, don't send retries through the same provider either.
I'm surprised you'd frequently get false positives. What regions were you sending to?
They were essentially unheard of with the UK networks and very rare with European networks. It was only Middle East and African networks that were troublesome, but they represented a tiny fraction of our traffic. Even then, false positives were rare compared to messages just not getting delivered.
Once again, if you are receiving texts that must mean you opted into them. User is expecting them and it’s different from a user receiving two texts never having signed up for them.
I do believe this technique uses some out of the box thinking and mostly DOES solve OPs problem.