Some suggestions:
1) plant deep-rooted legumes like crimson clover or hairy vetch. There are numerous variations on this theme.
2) plant a deep-rooted crop that likes to take up the nitrogen. Daikon radish, Buckwheat, certain grains come to mind. Again, numerous variations
These are two very easy options.
3) pile on wood chips and plant into the chips. Technically the plants will need to be planted under the wood chips, but the chips will break down surprisingly quickly
OR
4) Since you have those wood chips, try inoculating them with mushrooms--specifically Wine Caps. Nothing will turn woody mass into fertile garden bedding faster than Wine Caps
5) Make compost piles on the beds over winter. Don't get too concerned about getting browns & greens correctly balanced--just get the stuff piled up on the bed. As it slowly rots over winter, all the leachate will be drawn down by gravity into the soil beneath. In the Spring, maybe take whatever is left and pile up into a more properly constructed pile, but who cares a this point (you could also just chip the stuff in). All that leachate will do wonders for all over fertility.
6) If you feel industrious, you could make biochar and that in.
There are just a few easy-to-do steps that can work miracles on your garden bed. I can't speak highly enough for the Wine Caps or the impromptu compost pile that is just left to sit. And if you can get that pile a bit on the green side of things--that's actually pretty great as all of that green juice will work its way right into the soil beneath.
Good luck and please let us know how things work out.
Eric