I use Ooma VOIP service and you can forward calls to a different number (I use that occasionally). I don't use it but they also have an iOS / Android app which lets you make calls from your Ooma VOIP number. The FAQ says you can't call 911 with it, so that's smoke anyway.
Could just set up a phone farm like the Chinese run. They've got fun little adapters and boxes to get full "remote" control of a phone. Could rig one up for your own application, or maybe a pseudo-phone-RDP setup.
Get a Direct Inward Dialing (DID) number and a VoIP host that speaks SIP. Dunno about iOS, but Android has had native SIP support built in since Android 2.3 Gingerbread.
But those apps don't actually care about the phone number beyond the initial registration? Once registered, they work entirely via IP and don't know nor care which SIM is in your phone.
You will however have a problem with registering on those with a VoIP number - those ranges are generally blacklisted due to bad actors misusing those numbers for nefarious purposes.
With the idea being that I use a second phone to connect to my main phone over the internet.
This lets the phone number you actually have associated with you stay in the same fixed geographical location.
E.g. all calls are initiated by the primary phone and tunnelled over the internet to the disposable phone.