Is that really the easy bit to change? ISPs spend years trialling new hardware and software in their core. You go through numerous cheapo home routers over the lifetime of one of their chassis. You'll use whatever non-name box they send you, and you'll accept their regular OTA updates too, else you're on your own.
No. The router in your home would need to support IPv4x, or you would get no Internet connection. Why? Because IPv4x extends the address space "under" each IPv4 address -thus- competing with it for space. ISPs in areas with serious address pressure sure as fuck aren't going to be giving you IPv4 addresses anymore.
As I mentioned, similarly, ISPs will need to update their systems to handle IPv4x, because they are -at minimum- going to be doing IPv4x address management for their customers. They're probably going to -themselves- be working from IPv4x allocations. Maybe each ISP gets knocked down from several v4 /16s or maybe a couple of /20s to a handful of v4 /32s to carve up for v4x customer sites.
Your scheme has the adoption problems of IPv6, but even worse because it relies on reclaiming and repurposing IPv4 address space that's currently in use.