So to recap - I tried a patch repair kit but evidently the expansion tank is one of two types of plastic that that particular kit will not adhere to. Money wasted.

I tried an eBay expansion tank that arrived broken. Luckily they were very easy to deal with as they paid for return shipping and refunded me the entirety of my purchase price.

I purchased a used expansion tank off somebody that was parting out an X locally. I pulled the tank off myself and inspected it and it did not appear to be leaking. I filled it with water to test but it did not start leaking until it was under pressure. More money wasted.

Finally, I did what I KNEW I should have done to start with and ordered an expansion tank from Gary at Jabgits.com. I WAS worried initially as the expansion tank had poked holes in the box the same as the one from eBay had but the nipple had not broken off of this one. I do not know if this was a result of a higher quality product or less room to move around in the box but I spoke to Gary and we both believe some packaging material inside the primary box with the expansion tank would prevent it from rattling around in the box.
So long story short, get the good stuff to start with because these cars are very finicky when it comes to replacement parts. I feel I should have known this from past experience as this is my third Jaguar (second X-Type) but necessity being the mother of invention (I'm pretty strapped for money right now) I decided to try other things.

My morale is this, if you can afford the right stuff, get it. If you need to save up for a bit until you can afford it, it's worth it. Just my two cents!