You are concerned about not losing any additional height but Owens Corning foamular is available in 1-1/2" thickness and gives you an R value of 7.5. You barely exceed your 2" limit and gain 50% more R value. Another possibility might be to lay an electric in floor heat grid in the floor where you will primarily be standing. Another possibility if you still feel your feet chilled are these types of mats made for livestock. You can find them at farm supply stores that cater to livestock producers but they may or may not be readily found in your part of the country. Here's a link for a 2' x 4' size.
osbornelivestockequipment.com/product/stanfield-heat-pad-s2b4/