I'm wondering if 2DS and New 2DS XL are allowed. Are they?

Yes, they are. I believe that they don't appear as pickable platforms. But they are essentially their 3DS family equivalent.

The site listing is a little inconsistent but for what it's worth I added 2DS and 2DS XL as selections. Honestly didn't know they were options before, and (New) 3DS XL are not options, but oh well.