The Drop-Leaf Chair?  

Odder to me than the tablet -- a lecture-hall feature ? -- is the padded "collar" next to it . . .

Regarding the padded collar, it does make for a nice way to sit with one's elbows up on the top. But why it would be padded all the way around: I don't know. 
Is it crazy to entertain the idea that the chair was meant to be sat in frontwards and backwards?

Yes.  We had one of these on the forum a while back, I think.  What did we learn then ?  I've forgotten.

Oh really? I didn't have luck with my keywords when searching the forum. I do wonder what the take-away was in the previous post.

A couple more things of note: 
I've sat on the chair backwards and it feels right (which means nothing, I know)
There are two grommets where the metal rod support fits, suggesting the need to adjust. The second setting pitches the table upward. When I interacted with the table in that position, it was very similar to using a drafting table. 

Upward ?  Then it must be a "backwards chair," for use just as you describe.  Amazing. The cutouts in the seat and narrowly-placed rear legs support that idea.  
Enjoy (especially when the urge to write or draw takes you) . . . !

Interesting. Here are the two settings of the table:

Interesting.  A minor difference . . .

Found it.
It's the Frederik the VII chair by Hans Olsen and manufactured by M J Rasmussen. I believe the information to follow was sourced from a Mobilia issue. 
Apparently the Danish King Frederik VII liked to sit backwards. Hans Olsen is said to have been inspired by a chair at Rosenborg Castle in Copenhagen. I got some of this information (there's a bit more) from  http://sharplinesoldtimes.blogspot.com/
 

Great and unusual find!

great item, great sleuthing!