Larger Watch Bands for Series 4

Correct. Apple has a limit to the band sizes.

3rd party bands are plentiful. I can't really recommend any as I don't use them. You may need to look at reviews for them.

I know Amazon has some that are highly rated. (4.5 stars)

Carterjett Extra Large Nylon NATO Compatible Apple Watch Band 42mm XL - Amazon.com

I may receive some form of compensation, financial or otherwise, from my recommendation or link.

Any bands for other series watches in that length will work with the Series 4.

So if you already have bands that work for you with other Apple Watches, you can use those with the Series 4.