Screen and polarizer burn.

The answer is a big fat NO unless you find a donor :-(. Amazon devices are disposable, they do not sell parts and get around RtR by replacing the device in states with a parts supply loophole that is negligent. The other problem is the Kindle DX (mostly) met it's match at the hands of the 3G sunset in the US, which was ALL the carriers and Amazon when they shutdown 3G Whispernet; you can't connect them externally anymore. You can still sync books on a computer but that's it.
That said if you want to fix it, you can use this to your advantage; people will freaking GIVE AWAY duds with serious failures (ex: bad bords, swollen batteries, no charge, etc); as long as the screen works (and the keyboard and screen aren't one thing and both need to work) you're good to use the donor screen. However, this adds a second snafu... Supply vs demand; there are more working ones that can be rehabbed then buyers due to the lack of WiFi so pricing on this donor will need to match. The SAFEST way to do this is a motherboard transplant; do not remove the magnesium midframe if you can avoid it.

While there are no guides for the DX Wiki you selected, I can point you in the right direction on one I had to deal with due to data on the device (Kindle Keyboard 3G/bad battery); yes, I tried to fix it but there are no good batteries left for the 3G Kindles, even WiFi+3G: odds are, it's clipped together. Run an old credit/debit/gift card/unmarked blank/etc. across the edges, and if you run into any snags, use a guitar pick as needed. Some of the early, early ones used screws but the "sealed battery" generation almost always ends up being clipped shut. Take notes on what goes where. The new ones (roughly when they did away with the physical keyboard) are glued together abominations, so if you buy a new one please try and avoid an Amazon unit again unless you have a lot of their DRM protected ebooks. The only one I can think of that evaded the glue trap is the Voyage in the sense you could AT LEAST access some of it with little adhesive interference outside of the display; ALL of the newer ones with the adhesive front are sealed abominations you need to risk the screen or replace the bezel when it gets bent, OR it rejects any 3rd party battery you throw at it unless they spoof the Amazon vendor ID the Kindle is expecting, or both (usually both). The Kindle Keyboard 3G I had to scrap IS one of those "invalid battery" detector ones, so I'd battle several batteries; no thanks, I'll get a reader without 50 layers of DRM garbage.

It looks like yours is the clipped/door hybrid design? See here: Amazon Kindle DX LCDの交換.