If the sync chain is "working" as is, don't bother spending the money on it and, instead, get your drive-side chain, chain rings, and cassette squared away.
Sync chains either work or they don't and you can basically run a chain & the timing rings well beyond normal replacement points without any adverse effect so long as you keep the same "worn-out chain" on the same "worn-out timing rings".
Now, here's a neat trick that's unique to tandems: timing rings can be rotated front to back to get a "second life" out of them with a new sync chain in that, the front & back timing rings wear out different sides of the chain ring teeth. Therefore, instead of chucking them, if they aren't ramped or pinned, you can just remove, flip over, and re-install the timing rings on their respective cranks and essentially have a "like new" set of timing rings or, if they are ramped and pinned, move the front timing ring to the back and the back timing ring to the front and again, you have "like new" timing rings.
If this seems puzzling to you don't worry, it's a "tandem thing". The deal here is, the captain's timing rings wear out on the front side of the teeth from "pushing" and the stoker's timing rings wear on ont he back side of the teeth from "being pulled". Yes, that means what you think it means... don't go there. It is what it is. There are some rare exceptions where "super stokers" are actually more aggressive than the captains and in those cases stoker timing ring wear is far less pronounced than it is with most "average teams".