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I refer to this a lot as well:
basically Shimano 7-9 MTB and 7-10 road are all compatible with each other, and with SRAM you just match parts together according to whether it's "Exact Actuation" or "1:1 Actuation". I don't mess with Shimano 10 MTB, 11 road/MTB, or Campag
like I said though, I have got Exact Actuation and Shimano-compatible friction shifters to work. As you can see in those tables Shimano pull ratio is 1.7 and Exact Actuation derailleur shift ratio is 1.3 compared to 1:1 Actuation ratio of 1.1. So you can see I don't need to pull quite as much cable as you do to get through the whole cassette. Which'll be why mine works and yours doesn't.
Ultegra has the right ratios but as Tester says won't clear a big cassette. Your best bet would be a £15 9-speed Deore derailleur I would think. Several people on here use that with up to 11-40 even without a RoadLink. But you can buy an eBay RoadLink for £1 if you need it.
If you Google "turkey vulture gearing" you'll find an article that describes long cage 9-speed MTB derailleurs with front mechs and big cassettes. (website is dead, here is google cache version.) Those guys run 11-40 with 24/44 for a total of ~49 links wrapped by the derailleur. And someone in the Monstour or retro MTB thread had a Deore LX with 11-40, think it was a Marin with 3" tyres? (it was - here)
Edit: ah just realised I confused your total capacity for biggest sprocket. Tired today. But basically what I'm saying is get a long cage 9-speed MTB derailleur, they're cheap, sturdy, long enough to wrap all that chain and have compatible pull ratio
Edit: Also, with Dura-Ace DT shifters you can use them friction if the indexing is wrong. If you need to get something working ASAP just use your Ultegra derailleur, Dura-Ace shifters in friction mode, and whatever 8/9/10-speed cassette you have around that the derailleur clears.