You called the travel agent and the airline and got nowhere (for free) because they don't want to do this for free. $650 a person, or total (not counting dogs) does not sound crazy. For business class. Pay the fee vs. rolling dice for the next 3 months.

Unless people just have no desire to go on these segments in June such that the prices become give aways to fill the seats they are more likely to either a) go up in price or b) disappear entirely closer to departure.

It's not you and not the airline - this is how all airlines work. You want the ultimate flex when you travel, you can buy full fare tickets with unlimited changes and refunds but you will pay a whole lot more than that $650.

I do this cost/benefit analysis a lot because I fly a lot and change or cancel a lot, so I either buy full fare refundable/changeable business class fares or look at the cost of the insurance element (that's what full-fare tickets really are vs. restricted ones) if my odds of changing are pretty low. Or if it's a airline I might never fly again or soon and a parked credit might be lost money.

Example I am on a trip now which was $2,800 fully refundable while my D fare was $1,300. I did a change (added two days at the end) so they had to change from D to J for the return at a net new cost of $600. Total cost, $1,900, still $900 ahead.