Jay, glad to have been understood, even if only a little.
I met some ten years ago a group of Polish people in Milan, those were the nicest folks ever! We even continued to be pen-pals for some time. But unfortunately we barely understood each other - I think I'd understand Czech slightly better, unfortunately didn't have any opportunity so far.
However we have taken some letters from Czech orthography, we "borrowed" your "háček" in diacritic signs such as čšž so I reckon that at least in the written form we'd able to understand it better than Polish.