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What about a 9-speed medium cage Ultegra?
It will work with the lever, but you'll be over the limit of both total capacity and largest sprocket.
11-34 with the 34 taken off
If you're thinking of thinking of cutting the 34 off a 10-speed, you'll be disappointed again, the spacing is different and 9-speed lever/RD combo won't index properly.
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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.
@frankenbike @mdcc_tester bums, that’s annoying. Thought I’d check in case I’d done something wrong. What about a 9-speed medium cage Ultegra? I guess my next question is whether a medium cage derailleur can take a 40-tooth total difference from top to bottom [edit: sorry, it needs ~30 tooth total capacity], with an 11-30 cassette on the back (11-34 with the 34 taken off)