Warm ice is always alluring because it is so easy to get everything to stick, until the ice falls down. You are certainly not the first to mis-judge how soon it was coming down. Thankfully, you did not join some others in dying over making a poor choice. Accepting the rope was the only realistic option once you were in that situation and a "more experienced" climber would have fared no better given the conditions you found. The water chute you were in did not appear to lend itself to dry tooling or anything other than water/ice sliding once the ice stopped being climbable.