Yes, lime + sand ---> concrete. Or at least a good mortar for setting block. Chips and sawdust would be good, if you can work them in. As they break down, they will form humic acids which will neutralize the lime.
If you have cats, or if you have friends who have cats, collect up all the used cat litter that you can get
your hands on into a
bucket. For this purpose, the non-clumping kind of cat litter is better than the clumping kind. Put about 3" of the litter into a 5 gallon bucket and fill it most of the way with
water. Get one of those heavy duty paint mixer attachments for an electric drill and stir the whole mess up real good. You want to make a clay slurry. It may be good to mix it up, wait an hour or so, and come back and give it a second go-around with the mixer. Once you have some nice runny clay soup, pour this over your lime/sand concrete and work it in real good. You may have to do this a few times, but what will happen after a few applications is that all the sand grains will become coated with clay minerals, and they will no longer be cemented together. Clay/sand mixtures can also get hard and cemented together, but not nearly as bad as lime/sand mixtures, and they will fall apart much easier when they are thoroughly saturated.
Clay will help to bind up some of the calcium, and get you closer to the optimal spot in clay-sand-silt balance, but without any silt at all, clay has a tendency to sink to a level beneath the sand if you don't keep tilling and churning it up (which causes other problems that the no-till people can tell you about). Over time though, the organic matter that you add
should break down to silt sized particles and that will eventually get you to a nice soil tilth.
Lastly, adding
biochar is something that can also help here. Biochar does not make good aggregate when added to concrete, because it is friable and can break under stress, as in when a
root is trying to push through. Exactly what you want to happen in your soil. Figure out the total volume of your planting bed and try to add 2% of that as biochar. Again, repeated applications are probably better than trying to work it in all at once. The more often that you turn and mix this hardened mass that you have, the sooner it is going to break up and become soil. At that point you can look at things to do to build up the soil food web.