What is missing in the OP is what we read about in the last 24 hours:
"I am currently in the midst of crowdfunding my own smart contract network tailored to the needs of the music industry, called Tao. Tao is designed to execute Bitcoin transactions automatically in order to settle royalty payments."
"I had the opportunity to have a quick chat with Kim Dotcom and our goals are aligned. Tao and Kim's BitCache system stand to generate thousands of transactions per block, exceeding the tolerances calculated by SegWit. Lightning networks simply are not an applicable solution to our applications."
What I point out is these (or anything like these) are the killer applications for BTC-B(ig)B(blocks). These will generate value outside the BTC-S(mall)B(locks) branch and only in the BTC-BB
In this case, the BB branch can execute all txs the SB branch can and many more. Given the higher fee required to confirm on the SB branch, all transactions in the SB would confirm in the BB but not the reverse.
The fork coders could avoid and ignore the need to separate the txs in a branch from the tx in the other. This is matter for wallets.
Every tx would be validable in both branches, but once a tx is validated in the BB but not in the SB, the same bitcoin in the SB can not be used anymore in the BB.
If there is a demand for BTCs in the BB branch (to be used to pay for songs rights or downloads) the buyers will only have the BTC mined in the BB branch, and the BTC mined before the fork and not splitted. More pre-fork BTC are used in the BB-branch to pay for small transactions with small fees (outstripping the ability of the SB-branch to keep up and splitting, de facto, the coins in two different chains) more demand there will be and less BTC will be available to be dumped in the new chain from the old chain.
It don't matter if the SB-branch split the coins and dump them on the BB-chain, because the use case will anyway support a price different from zero and accepting the transactions in the other branch (valid in both of the branches) as valid will always give something to mine.
The problem is protecting the branch from a 51% attack and the initial change of difficulty, but there are pretty easy ways to do it with small changes to the PoW and rules to accept new blocks.
As the use increase, the price of the BB-BTC would continue to rise against the SM-BTC.