I grew up helping run a pick your own strawberry farm. As someone who
also just lost almost an ENTIRE batch of store bought berries to mold, I'm
also interested in this.
I'm surprised that no one has mentioned what is probably the most
efficient way to have your berries last longer - grow your own. The main
reason why strawberries from the store mold so fast is that they have
already been off of the plant for some time - perhaps 2 or even 3 days -
before you buy them. Strawberries are not known for lasting that long in
storage anyway, so by the time you have them in the fridge for 2 days, they
could be 5 days old already. Pick your own fresh fruits, and they will
probably last twice as long or more, and also be tastier - since they will
be more ripe when picked.
You said you don't want to consider freezing. Have you considered drying
them? I have cut up strawberries, plus made fruit leather with a convection
oven. It is very tasty, and lasts for years. You could also can the fruit.
If you want store bought for fresh eating, then I second the idea
presented earlier about cutting them up, and sloshing around some of that
lemon juice concentrate on the pieces, or even mashing them a bit and adding
lemon juice. The acidity will inhibit mold growth, and then you can add a
bit of sugar if you want when eating them.
Of course, canning is also an option, but they tend to lose some texture
from the high heat involved. Freezing is often a good option.