You can still use it on the garden when the garden is already growing. Break it up into small amounts and put it on top of the soil around your plants. Give the garden a good water before putting it on. If you have roses, don't put the hay right against the stem. Leave a small gap around. It can rot them if it's close. You don't have to leave much gap, and inch or 2 is enough. Once you've put it on, the garden will look great! Once you've finished admiring it, give the garden another water so the alfalfa gets wet and the water runs through it. Not only will your gardens look great, you won't need to water them as much because the hay will help keep the moisture in the ground. If you wanted to add more plants, just push a bit aside to make a gap and put the new plant in. It doesn't matter if it never gets mixed in with the soil underneath. It will break down and when you water, it takes the nutrients down into the soil. You'll find over time though, if you're replacing plants, it will eventually all get dug in anyway.
You've done the right thing not feeding it to any of the animals. There's been a discussion on the sheep forum about hay prices, can I ask how much you pay for a bale of alfalfa hay? The prices have varied dramatically all over the US, so it will be interesting to see what you pay for it in NC.
Jane
PS: I got your email, just need to find a few mins to reply. Hopefully in the next day or 2.