Thanks for your suggestions, I like the strategy.

In the meantime, I also managed to get confirmation from SWISS via X:
"Please be advised that if you have purchased a classic ticket that includes 23 kg of checked baggage, you are allowed to substitute your golf equipment for that checked baggage, provided it does not exceed 23 kg in weight and the dimensions of 200 cm. "

It took a few attempts, though.
As you mentioned, many agents are not very capable, one even stated that "rule regarding free baggage applies solely to ski equipment." , which clearly contradicts what is advertised on their website.