John,
I have also been using the Red River 7x10" Pecos River Gloss pre-scored cards for many years on an Epson 3800. My experience is similar to Brad's - the print quality is excellent, but the multiple sheet feed is sometimes unreliable. In my case, it would work most of the time, but you would have to keep an eye on it for the inevitable miss feed. Humidity probably plays a role in this. I don't recall ever printing on the inside of the cards, so I can't help you there.
Coincidentally, I just replaced the 3800 with a Canon 24" iPF6400, which can't load sheets under 8" width or height, so I can't use the stock of 7x10" cards I have. I ordered the 8.5x11" version of those cards, and while they print fine and the quality is also excellent, I wouldn't want to have to fulfill a large card order manually feeding small sheets on this printer. I know I could print multiple cards on a roll and then trim them and score them manually, but frankly that's too much work when the pre-scored cards are available
So, I find myself in the spot as you. The P800 is probably overkill since I have the large-format printer. However, the P600 would seem to be a good choice for printing smaller cut sheets like cards.
-Scott