I would note that the BLM warns you about possible ice on the Green River in March in Deso-Gray.
Deso-Gray is lower in elevation than Lodore, and further south, so Lodore could be colder and have more ice. On the other hand, it is just below the dam, so that could make a difference.
Call Kelly at Dinosaur NP before noon, 970 374-2468, she is probably the best source on Lodore, she has been on that job for a while.
You might look at the San Juan River in southern Utah as an alternative, lower and further south than most options. Those permits are not usually that hard to get, I understand, especially off season. I have done that river in April, not bad.
The Salt river in Arizona is an alternative, further south, but you have already missed the lottery, some of my friends have launch dates. I have heard some folks talking up the Verde, but I know little about it, except there is no permit required. Arizona is a long way, but if you want warmth and sun.....
If you want big waves, look at Cataract canyon downstream from Moab Utah, although March would be lower flow. Permits are there for the asking, anytime.
These are some thoughts, I am sure that other people will have good ideas.