My wife and I alternate and handle conflicts by exception. Meaning, if we have a conflict the other person subs in. I think calendaring things around your home schedule will be hard for the 'things'. Like, a lot of our evening activities are scheduled events that we can't control (concert, theater, etc) or even a group (dad's dinner, etc) and the occasional work stuff. Anyways, I just think it would be hard to plan for the home duties as a conflict and instead we try to sub in for each other and shoot for something that 'feels fair' over time instead of quantitatively fair on a tracker. I'm all for building tools for youself so if you think this would be of use then that's awesome, just thought I'd share my 2 cents on the 'problem space' :)
Also, FWIW, I think I'm the one that is in the deficit of fair although dad's usually get a bad rep in this regard. I end up doing a lot more night time reps because she does frequent girls nights and has multiple friend groups she's trying to stay engaged with and is in a theater group and mahjong group, etc. However, I balance it with my occasional "take an entire day" to myself. Stuff like this is hard to track and why I think it's important to shoot for what 'feels fair' and make sure you talk about it occasionally so nobody suddenly has repressed feelings of inequality.