The way I understood it was that it is supposed to be that people on the old chain can still use Bitcoin normally.
No, a hardfork requires
everyone to upgrade to a new client. After a hardfork old clients will outright reject the new chain.
Which is why this is a hard fork. Old clients will outright reject the new chain with the larger blocks.
They will accept the majority hash power attacks against their own chain, but that is a separate chain with separate rules. They would have to deal with this the same way they would deal with any majority hash power attack that refuses to confirm transactions.
If that does not happen, and if a significant portion of the hashpower refuses to upgrade, then Bitcoin will split into two completing cryptocurrenies that can co-exist forever. This is the worst-case scenario.
Correct, and this is what your proposal does.
If a "significant portion of the hashpower refuses to upgrade" to your proposal, then all they have to do is had code in a rejection of one of your blocks and "Bitcoin will split into two completing cryptocurrenies that can co-exist forever".
I'm curious, how does your intended solution expect to deal with the situation where the old format has a longer chain? This would mean that the old network would reject the transformed chain, but how would your system be aware that the transformed chain was rejected and what would it do with all those transactions that had been confirmed in it's big block chain?