That rear derailleur appears to be a 9 speed 7700 short cage. This won't work with a 28 tooth I don't think very well. You need a triple compatible short or long cage RD for that. The same era replacement would be the 7703 which does work with triple cranks and up like a 27 or 28 in the back. You could also get a used Ultegra RD-6503 or RD 6603 on there and be able to handle the bigger rear (low) cassette cog.

That rear derailleur looks fine to me, that fact that the body is moved so far forward and adequately wrapping chain is a good thing. If it makes you feel better you might try removing one or two links from the chain to pull the lower cage out to an orientation that looks better to your eye but either way I would think its OK.

One last suggestion is to keep the current Dura Ace short cage with tight 9 speed cluster and just change your cranks instead. You can order a New Ace compact crank or get a used compact by Shimano or some other company that should work. The smaller front chainring afforded by the smaller BCD (bolt circle distance) lets you run like a 34 tooth or 36 tooth small chainring with a 50 tooth big chainring. Personally, I ride triples and haven't officially road tested a compact double as proposed but I imagine it would be the best of both worlds: close ratio rear cog spacing that will allow tight control over your cadence as you get more fit, and the nice combination of chainrings of say 36/50 will give you enough of a low gear to climb good sized hills, the 50x12 or 50x13 biggest gear seems plenty big enough to spin up near 40 MPH on steep downhills ( at a cadence over 120?). At speeds above this on wicked downhills, you're going to be coasting anyway.