I cannot speak directly to highly sensitive skin and front loads. That being said, I know good number of people with sensitive skin (things like cannot wear dry cleaned clothes or have to use unscented perfume) and they all have front loaders and none of them complain. I do not know if they double rinse or not. They have a bunch of different brands/models and the only complaints I hear are the general washing machine one.
YMMV.
Edit: I was pondering this a bit more and I wanted add a couple things.
First, I did a little googling and there appears to be a pretty agreed upon hierarchy of water using devices; first is the toilet, then is the shower, then faucets, then washing machine ... there is some shifting as you go lower, but the first 3 or 4 are pretty consistent. You've already addressed the shower and are discussing the washing machine. I would suggest you look at toilets and faucets as a potential for upgrading to low flow/volume as well.
Second, those lists also have leaks surprisingly high for the "average" home. While not stated, I suspect this is because if a home has an undetected leak it can really bring up the average. While nothing you have makes me think you have a leak, you could do two tests. One shut everything off in the house (make sure you get any automatic things like ice makers) and check the water meter a few times over the course of many hours to see if it budges. If if does and you have a whole house shut off try turning that off and repeating. (if the meter budges with the house in the off position you may have a leak in the pipe between the house and the meter, if it only budges with devices in the house off you may have a leak inside the house).
Third, I just looked up the current water and sewer rates for the last place I had both ... a 3500 gallon bill would come out roughly to $15 for water and $45 for sewage. If that ratio hold for you, 3/4s of you bill is sewage. Based on what you have said it looks like ~10% of your yearly water use is your garden, which means ~7.5% of your water bill is sewage costs for water that does not go into the sewer system. As encouraged, I would look at ways to reduce that cost.