I have done the Tat-Alsek but not Turnback Canyon. We did the trip in August and water was dropping, we had trouble taking out near the airstrip. The rivers sometimes have 2 peaks one for snow and one for glacial melt so you might want to check the hydrographs. You can also get sudden surges when glacial dams give way. You should contact the Park Service and the Canadian Parks, they were extremely knowledgeable and helpful. I also suggestion you contact this outfitter. Brabazon Rafters' Support Services
He is at Dry Bay take out and knows all the local bush plane pilots, he was essential in helping us getting out. We had a large plane scheduled to pick us up in Dry Bay but due to weather they could not land. They flew to Yakutat and we had bush pilots shuttle (we had to hire on the spot) to take our stuff to Yakutat from Dry Bay. Yakutat is likely your most reliable alternative for getting out, hire bush pilots to take your gear. You will need someone who knows and has communications with the pilots. In SE Alaska you must be flexible with your take out it all depends on weather. Pat is a character but he was extremely helpful.