tow

You are at the bare minimum in terms of capability.  I'm not an expert, or even competent at dealing with technical specs, but it sounds like your Evoque will work, but I'd be surprised if you'll be happy with it as a tow vehicle for the Pod.  Towing is about safety more than anything.  You will almost certainly need a weight distributing hitch (which adds weight that counts against your load) and sway control to be safe.  It goes without saying, but here I go anyway, that a brake controller is essential for safety and legality.  You are still going to be very much aware of your extra load, and you won't be doing your engine or transmission any favors.

On smooth roads you'll probably be fine.  On long hills, or mountain passes, you will probably be cursing the Evoque, the Pod, yourself, or something.  A transmission cooler would probably be in order.

BC to AZ is a long trip and it's not all down hill.

I think people pull pods with things like this, but if you do and ever try pulling the pod with an 8 cylinder truck or SUV, you will never go back.  If you have a choice, I'd really recommend something with at least a 5000 lb towing capacity out of the box. 

If it's in the budget, in my opinion you'll enjoy the trip a lot more with a larger TV.

TT

It's not going to be the weight alone, it's also about frontal area, and as aero as a pod looks.. they are not. Your owners manual may very well address this, mine does.

I suspect that trip, with that combination of trailer and tow vehicle would be pretty hard on everybody and everything, involved.

If you can rent locally that may be a better option.  Remember to take into the equation the amount of gas you save by not towing it all the way there and back at 12 mpg (US) or less.  Probably half of what you normally get.

It would be nice to know which engine was in the Rover used for that test, as it's a eurospec, it could be the bigger diesel.. would make a difference I think.

Some receivers (the square part mounted on the TV) are slightly too big, so when the hitch is mounted it can move slightly.  That will sound like a thump on bumps and uneven roads because as the pod's tongue rises the hitch can wiggle around momentarily.  Usually when you have a WDH in place it won't thump when starting or stopping because it is maintaining upward pressure on the hitch.  With your hitch in place but not hooked to the pod, can you wiggle it around?