isn't the 50Ω cable messing things up in general?
No, the important thing is the coax - it has a fixed 50 ohm characteristic impedance and therefore, to prevent reflections from the antenna (35 ohms), you should use an RF transformer to back-convert 35 ohms to 50 ohms. This then matches the antenna to 50 ohms.
A simple 1.2:1 step down RF transformer will do this because the square root of the impedance ratio is 1.195 and 1.2:1 is good enough. This transformer needs to be placed at the antenna end of the coax. The voltage step-down is towards the antenna.
So now, your transmitter will see 50 ohms and you can stop at this point. 12 turns to 10 turns seems nearly perfect at the antenna end.
However, if you truly want to maximize power transfer then you can step up (using another RF transformer at the amplifier end) the 4 ohm amplifier output to circa 50 ohms. The square root of the impedance ratio is 3.54 so a 10:35 ratio step up transformer would be good if you really wanted to push things. Of course you may be limited by power output and by legislation.
General idea: -
Transformer design needs care and I've estimated the number of turns based on good RF ferrite material and a typical pot-core. The devil, as always, is in the detail and, this design should be undertaken methodically so as to produce sufficient magnetization inductance in order to minimize unnecessary amplifier loading.