Sorry, I don't know about needlepoint.... I can't do it because of my hands and the old carpal tunnel. So I never learned it.
I used to crochet and embroider...but those days are long gone.

I suspect what you bought is not waterproof. That is why it stretched out.

Try looking at a Google search of "plastic mesh"... I did a quick one and only found expensive stuff.

There are nylon screens made you know for windows, in the hardware departments. That might work for you, without cutting you up.
They use these for window screens when metal types are not wanted. I don't think they are expensive at all. But I'd wash them before using for food purposes. Who knows what might be on them from the factory etc. ???

Here is a trivia factoid. You know what is used to screen urine for kidney stones/crystals? PantyHose!