Sick days are an effective tool all crew (captains) need to utilise. Manage your fatigue/92 hrs a month with a sick day or two a month (preferably near the end of the month to mitigate roster recovery), its a message the company gets. No manager will put in writing they want you to fly sick or fatigued. GCAA is on the airlines (EK and unmentionable) side but they won't tolerate breaking the rules that blatantly as they strive for their ICAO recognition.
The pressure the company puts on you is expected: removal of self certification , delayed upgrade, denied captain transition from A330/340 to A380 etc.
Go to the clinic, certify your lack or sleep from back to back roster and manage your 92 hrs a month. Get your upgrade, manage your roster.
Its not the answer, its a message to management.
Word is 10 freighter flights have already been parked/pawned off on other contractors due lack of crew. Call sick and this may translate through to Pax flights. The management will sit up. Heads will roll if pax flights are parked. fight back.