The plot goes back up for sale again in the next lottery period if it is not claimed by the holder of the winning entry.

Your FC is not the holder/owner of the entry. The former member is. If they had the winning ticket, you're out of luck. You'll have to try again once the lottery resumes (hopefully a different member of your FC has the winning entry and that won't be necessary).

If they did have the winning entry, they wouldn't be able to use it for a different FC unless they've passed the 30 day waiting period before the claim period expires and came up with the gil to pay for it (since you said they took the refund already). Under normal circumstances, this would be impossible (the claim period is only supposed to be 4 days).

Considering how long the claim period has been extended as SE works to implement the fix, there's a slight chance that anyone that had purchased an entry for a FC in the initial lottery then left and joined a new FC as the claim period began may have opportunity to purchase for their new FC if they had the winning ticket.

Contacting the GMs wouldn't accomplish anything since they don't have the power to transfer ownership of an entry to another player. The most they could do would be investigate if the former member did have the winning entry and was able to purchase the plot for a different FC due to the extended claim period. It's anyone's guess how SE would choose to handle such an event on the remote chance it happens. But it still wouldn't get your FC that plot.