hi
6603 is another good option.
6703 won't have any compatibility issues with your 7803 shifters.

To me, its too hard to read the label on the RD so I don't care what it says. There are some slightly better features on DA compared to Ultegra, such as pulley washers rather than bushings. Get DA if you like these features, not for the label.

Get what you can find for a reasonable price, and include the 6603 in your search.
A small advantage of the 6703 would be compatibility with the newer expanded cassette sizes (11-28). Old 6600 and 7800 series RDs aren't compatible with the 11 tooth or 28 tooth cassette ranges.

I always check the compatibility charts and this is what they say about your decision. (extrapolating for triples a bit since they're not on the chart, but I'm running a 6603 myself as well).