My two penneth. I think filling the tyre stack with the right soil might prove more expensive than getting the wood.
Think about this one.
Can you make a strong wire fence to take the foliage..not the weight of the fruit, just the foliage, something like a bean fence or a wigwam, then when the fruit start to grow instead of slinging them in tights etc you can build them little platforms,about 2 1/2 feet off the ground. Imagine a strong flat bird table on a pedestal, the fruit can be placed on when quite small and even the heavy ones will not be a problem. As they grow they are protected from the slugs and take up much less room.It can work very well with the heavier varieties of squash. The lighter weight ones will be ok fastened to the wire with the tights.The squash grow clean and safe and most of the weight is on the pedestal not the fence.
Re tyres, it is a personal thing, but I am always a bit nervous about veggies growing in rubber.
It is just a couple of thoughts.
Have fun with your squash.
XX Jeannine