That's cool and all, but end-user edge routers are absolutely going to have to be updated to handle "IPv4x". Why? Because the entire point of IPvNext is to address address space exhaustion, their ISP will stop giving them IPv4 addresses.
This means that the ISP is also going to have to update significant parts of their systems to handle "IPv4x" packets, because they're going to have to handle customer site address management. The only thing that doesn't have to change is the easiest part of the system to get changed... the core routers and associated infrastructure.
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.