[mothered]

How much work will a SE like this take? It's over $3,000 so I'd assume quite a bit.

It all comes down to your method. For Instance, using the DNA for an Item of this value, Is almost guaranteed to open an Investigation and It will be quite a lengthy process. They will cross-check every minute detail, as well as request a police report. Do not use this method. As mentioned, the wrong Item received Is well-suited. Obviously, It must be roughly the same size & weight.

Is it alright to attempt to SE an item like this even though I have no other purchases even near this price?

As far as Amazon Is concerned, your SE Is purchased for legit reasons and you should treat It as such by not questioning assumptions. If you ordered this and "legitimately" submitted a claim for a faulty Item, would you be asking the above question? I didn't think so.

Would using my Amazon Card be a bad idea for this?

In short, the payment system Is Immaterial.

What method of payment should I use? I don't have $4k to blow on this from a debit card, so maybe a credit card?

I'm not a financial adviser, just here to assist with your SE.