Yes, I use fresh straw bales but put them in place in the fall so they can break down inside by spring when I am ready to plant. Then I cut holes in them, add potting mix (Pro-Mix) or my own mix of compost, coir, and perlite plus organic fertilizers and plant. My tomatoes get huge and the eggplants really seem to like them. If you are interested check out the Strawbale Gardening forum: http://davesgarden.com/community/forums/f/strawbale/all/240 I linked you to page 1 where you can start to read the techniques. Since it will take a long time I am also d-mailing you a copy of my own synopsis I created after reading through all those pages!!! I tweak it every year as I learn new things. I now try to get alfalfa hay bales instead because they contain nitrogen. I use only organic fertilizers. After the initial planting using granular I then continue to feed with organic liquid fertilizers (Aggrand) which is made up primarily of fish products. They also have a liquid bonemeal, lime and kelp. I use straw also in the garden for my bedding and do have to deal with straw weeds so may start adding some more of the wood chips. But the bales break down into wonderful compost after a year or two so will always keep using them. Once the bales heat up and begin to break down the straw seedlings are no longer such a problem in the bales. I just give them a good "haircut" when they get too long. Later I can pull them out easily as the bales soften.
Your garden sounds enviable! I have been adding wood chips like crazy to all my flower beds at 18 5 gallon buckets at a time. My husband shovels the chips into the buckets, I load them onto my DR wagon and cart them back to the house and gardens. We had drought for 6 weeks and now non-stop rain and the chips are making a huge difference so that keeps the inspiration going. But I probably should start using them more in the veggie garden. Good luck on finding the rabbit manure - it is great stuff. I always add it to my compost before using the compost and the flowers love it!!