Hi! I've had problems mulching with new beds in the spring because it often slows down the warming up of the soil! Since it's February and you don't have time to do a sheet-compost system and wait (although that may be a good alternative if you can stand the wait), this is what I'd suggest. Tilling, or even hand-working the area, being very careful not to walk on anything once it's 'earthed'. Then take a shovel and scoop out the paths in front of you, one scoop to one side, one to the other side. In effect you are shaping the beds by only walking on the path. Ta da! It's raised beds all around.
Then what I've done is start seeds, do transplants, etc. according to soil warmage (this technique also speeds that up). And then mulch around the plants once they're 'up' enough. Also by this time there's some grass-mowing going on somewhere, so I leave that on the lawn to dry up a bit, and then mulch around the plants with grass-clippings.
I hope these suggestions help
