On Swiss, book exact same itinerary as close as possible to original travel dates, but on one or more flights that forces the reservation into the refundable RBD you want because lowest is unavailable on those flights (use EF to help you find flights with no lowest RBD inventories). Once ticketed, call in to change to the dates you want. Make sure ticket gets reissued and you get the new ticket number.

Difference vs just calling in is no need to hand over CC data to agent (if you do it correctly) and no risk of agent making typo's in names or other vital data. Also no service fee and time spent on the phone will be significantly less. You have more control.

Note to have a "zero charge" change make sure the itinerary is exactly the same and book as close to your desired travel dates (taxes fluctuate depending on date).