I would look at everything that changes with that much gravity change.
If you break it down by year that is a .5% gravity change every year up or down and some unlucky people at the end of a cycle feel it increase and decrease over their lifetime. It doesn't seem like a lot but people would go from 50 lbs to 200 lbs in the same timeframe if they weighed 100lbs. If people live 50 years they can expect to lose or gain 25lbs, for a 100lb person. Not a big deal. I don't think most people will require too much change for this to be handled but the longer they live the more uncomfortable they will be if it is getting heavier or more lively if it is decreasing.
Air pressure follows the same change. It will go from 45PSI to 15PSI. That is the equivalent of going from 7,000 feet underwater to 18,000 feet up. So air pressure is a real problem. More so for plant life than for animals that can just go higher into the hills if needed. In a 50-year life span that is a change of 0.15PSI a year or 7.5PSI in total. Again it is something to worry about in plant life.
There is a chance that trees will grow like crazy in low gravity years then the upper branches die off as the gravity increases. Maybe it segments the body of the tree so that it has rings like bamboo with each level mostly independent of the lower levels for when the gravity stops water from going up to the higher branches. Or maybe trees begin to droop or grow out so it is easier to get water to the branches instead of up.
So I think life on this world would have an extra sense organ like you mentioned, that has a pressure chamber that acts as a barometer. The organ can tell when the pressure is getting higher or lower and can influence live to move to higher altitudes or lower ones. Maybe a slow migration of animals over the years.
Bone density and muscle density may also be changed as you mentioned but even on Earth people born in higher altitudes have different lung capacity and increased red blood cells. So we can assume that not much change will be needed to deal with the air unless they live really long.
So I think your idea works fine. The gestation period would be the same just the result at the end would be different.