We have tried Weeb TV but the service is too slow, the video constantly needs to buffer
You should change the location of the Weeb server (in my account tab) - for example if you live in the States, the data center location should be set on United States (Washington) - the service will be much smoother.
Does anyone out there know of any good TV services that offer Polish TV?
Besides the satellite providers there's also the Netflix with bunch of Polish movies and shows. You can also save a lot when using free sites like tvzafree.pl or others, but the quality and convenience isn't great in that case.