FYI: This was in regards to a "Vanilla" game.
UPDATE: My computer died, and I lost my saved game.
Although I wasn't able to get this exact scenerio back, I have experimented a few times to see how well your advice would work.
1. I was able to snag 4 slaves from the surrounding Civs, and then attempted to clear a path through the jungle. Even with 12 industrious workers, irrigating a path through jungle takes a long time. Also: I needed to protect my worker stack with several units because the barbarians were all over the place. I rate this strategy D+ with industrious, and F otherwise.
2. Instead of workers, I tried again with settlers, and built a line of cities through the jungle. Bad idea. I was forced to spread my armies across a half-dozen worthless cities because the other civs tried to steal them as soon as they reached size 2. Also, because they were surrounded by jungle, they kept shrinking from disease. I ended up with a German camp in the middle of my irrigation line before I was able to bring water back to my original territory. F-
3. I researched Iron Working, developed my arid homeland, and then pumped out a stack of swordsmen to conquer my continent. This was much, much faster than an army of workers, and unlike the line-of-cities strategy, I maintained my population and production power. C+
4. I popped a city at the edge of the foreign irrigation, used a rush-build temple and library to generate culture, and "stole" a few boxes of irrigation. I then worked backward from this colony, putting lots of cities close together to get rid of as much jungle as possible, and using workers to irrigate back to my capital. This was much faster than #1 because I used 100% homegrown labor. Also, by the time I had irrigated the first "colony", it was a size 4, and became my new worker farm. By the time I returned to the capital, I had 40+ workers, and my neighbors were all in awe of my culture (rush). B+
5. I held a grudge for 6,000 years, and then obliterated the foreign farmlands with nukes. Not very helpful to my early-game strategy, but very, very satisfying. A+++.