Any chance of changing the drop rate so they are accumulated over time?
E.G. If you kill general Oni 200 times the drop rate for the gold weapon increases to 30%. After 300 times it is 100%, then it resets to 0 again.
Possibly only for bosses and gold weapons.
Edit: Another idea I thought of before is for your pet to be intelligent and somehow guide you towards the bosses you need... eg he knows your gear and what regents you need to upgrade your gear, then he can suggest to you which boss to fight. Or, if you need more xp he can let you know which map/tower will give most xp for you. Also your pet can bring luck where you have a higher chance of finding the regents you actually need, instead of sigils all the time..