It's important to note that if the hard fork happens, core will likely have 25% or less the hash power meaning block confirmation time will likely jump to 40 minutes or more on average. It will take at least one difficulty period, possibly two, for it to get back to a difficulty level where it is at 10 minute block time and it will be susceptible to 51% attacks from the BU miners, though I hope they do not do that. It is however a very real risk and one should always be aware of possible threats.
While the block confirmation time is so long, the core fork will be particularly vulnerable to DoS attacks on its blockchain and I suspect they will happen simply because some mean people will see DoS attacks as a fun way to get rid of their core fork coins. I do not approve of such behavior but I suspect it will happen.
As such, I do not think the core fork will survive very long.
Simple fix to the delay (assuming your scenario plays out above) is to hard fork to lower the difficulty enough such that it would be around the same amount of time to adjust with the current hash power core has.
Likely within core there would probably be a unanimous vote to do such a change to lower the difficulty.
There obviously are more dimensions to the scenario than you've thought out.
