I have no experience with those. That seems like a disaster waiting to happen. But adding a hood and venting system would likely cost more than a new range. The problem fixes itself if they ban new stoves. It is not immediate, but then your solution has the major problem that a lot of the burnt gases will escape to the room even if vented.
"your solution has the major problem that a lot of the burnt gases will escape to the room even if vented"
Mine don't. Hardly even any food odors escape into the room when cooking.
As for ventless heaters.....
Lets say you use your gas cook stove 3 hours a day.(and that's more than most use it)
3x365=1,095 hours
A ventless heater runs on average 20 minutes every hour for 24 hours.(that's only kicking on twice for 10 minutes each hour). It will be more than that depending on temp, insulation, etc.
That's 8 hours a day for lets say 5 months during the cold months.
8x153=1224 and that's not counting the pilot light that burns 24/7 during those five months.
So which is worse?