I'm advocating and helping networks to migrate to IPv6, but I'll say that IPv6 was rather a rats-nest design that shot itself in the foot. It's elegant sure, but as Torvalds would say to critics about his frequent use of goto, it's theoretically good but not sound engineering practice.

The thing is we would be addressing in 128-bit IP already if it was done the BGP way: just minimising the necessary changes to implement it. Look at the effectiveness of Itanium versus AMD64 at migrating customers: IPv6 feels like Itanium, while extended ASes work more like AMD64. Whoever designed IPv6 was focused too much at the theoreticals, than looking at what the real world is and then designing around it.

Can you suggest a way of extending v4's address space that works like BGP or AMD64 do?

I've asked a lot of people this question, and the only answers I've ever gotten are either impossible or already implemented by v6. Perhaps you will be the person to finally explain how to do it -- but as far as I can tell, it's just not possible, and I don't think it's fair to criticise v6 for not doing the impossible.

Do we have anything for IPv4 similar to AMD64?

Or are we forever stuck with either going all in to IPv6 or the current hybrid?

Nope, but we're deep in IPv6 anyways so the best course of action is to finish that, just be careful of the pitfalls and not devolving into silliness like this peering fight: https://www.theregister.com/2018/08/28/ipv6_peering_squabble...