Which Epson printers have straight feed for thicker, rigid media?

I know my 3880 will allow printing on thicker media (up to 1.3mm I think), which feeds and runs straight through the printer without having to bend.

I think the 3000 and the 2880 have manual feeds which allow the same thing. Are there other Epson tabletop models--smaller or larger--which allow for "straight" feeding to print thick and/or rigid media?

Regards, David.