the original putty that is applied in such screen installations is actually plumbers putty - I have installed a few old model mercedes benz screens and they are also in the same league as this.
firstly - yes the rubbers need to be replaced with new.
secondly a good cleaning and priming of the pinch welds of the screen frame and then spending some quality juvenile time rolling up putty and sticking it on the body and then installing and pulling the install ropes would make quick work.