That works great, but usually DCs are set as 8+proficiency bonus+stat mod. Not a big change (sorry for nitpicking), but it does give higher CR creatures a bit more of a bump up in threat. I find they need any help they can get as characters level.My player suggested using a static DC to resist/escape the garrote = 10 + DEX or STR, instead of an opposed check like grappling normally uses.
My 2cp for strangling/suffocating:
I always split them into either exploration or combat
Exploration: You can hold your breath for a number of minutes = 1 + Con mod (min. 1)
Combat: You can hold your breath for a number of rounds = 1 + Con mod (min. 1)
You can explain it however you want, but how I picture it matches up well enough in life to keep my verisimilitude - I like to picture it in combat as heavy exertion and panicking as your blood flow is interrupted by an attacker, which can knock someone unconscious in seconds in real life (as a BJJ practitioner I can vouch for this, it is extremely dangerous). In exploration you can be a bit calmer and hold your breath for minutes at a time - certain people have trained to do it for even longer!
Without getting into anything, this subject does touch on a lot of current issues going on - I hope everyone is able to find joy and safety in whatever gaming groups or areas you play in!