Hi Jakub,
I can confirm that Peters J-Pole diagram works very well with the 300 Ohm twin-lead by DX-wire.de . One remark - and it might be obvious - I had troubles making a good J-Pole and the problem was actually the coax cable which was of poor quality.
Thanks to Peter for the troubleshooting we did together
So a good coax (H155, or for lightweight: RG316 or RG-188) that is having low losses on 2m are mandatory to make it work properly.
73 Joe