I can't get the link to work. I tried copying and pasting it myself and it didn't work for me either!
I would either pack the booster in a hard suitcase, surrounded by soft items (which wouldn't give you the exemption) or pack the top (if it's a high-backed booster) and bring the bottom on board as a carry-on item. You can't use it on the flight but at least you'd know it would get there and it would fit in the overhead.
If you check it, I would put it in a clear bag, so that they can see what it is, and maybe even bubble wrap. Try to get it treated as a "delicate" item.
Boosters are easier to buy and replace than car seats. In worse came to worse, and it didn't arrive, one of you could run out and buy one. Still would work out cheaper than renting one!