I would point you to Gen MacKenzie's interviews as the reference on that question, I would just be regurgitating his views.
He says that a sustained coastal invasion is not necessary. Raids would be necessary to destroy any buried weapons, but these troops wouldn't need to stay there.
Other than this you need more of what they were already doing, "shaping operations" as he calls it, which is ISR drones overhead and lots of bombing/strafing runs.
Eventually, because they don't have a remaining industrial base and cannot effectively replenish their stocks (excepting more simple one way attack drones), they will lack the ability to project enough power beyond their borders to keep the strait closed.
Operation Praying Mantis is a somewhat dated case study, but still required reading.
The reason it's so expensive should be more intuitively obvious - interceptors are expensive and are needed to pace China, and a few more months of closure is significant inflation before the midterms.
