I too have issues keeping my extremities warm and they'll often hurt without proper care or activity, even in moderately cool temps.
This article hits my system spot on, but also links to some other article for cold weather footwear that may work for you too.
Specifically, if it's cold I expect my feet to get wet somehow (water, snow, simple condensation and sweat). So if my feet are going to be at least clammy, might as well keep them warm. Neoprene socks work really well. I've hiked all day with my feet submerged in 40-50f water and not had my feet feel particularly cold. That's with simple 3oz NRS hydroskin socks (only 0.5mm thick with a thin fleece lining). So if you went with beefier neoprene, you'll be warmer (and heavier). I find this works well as long as I give my feet time to dry once settled into camp, before sticking them into socks and my sleeping bag. With cool weather it usually doesn't take my feet too long to fully dry out, where I live that is.
As others mentioned, your fluffy socks may also be TOO thick, enough so that you're cutting circulation to your feet. It's surprising how little pressure is necessary to reduce blood flow. I tend to keep my laces much looser or size up my footwear during cool temps to ensure adequate blood flow (and warmth!). Since you don't want to carry much more gear, I would suggest just trying the bread bags. The VBL effect will be the same as neoprene (although I think neoprene is warmer per thickness/weight than big fluffy sock and a VBL). Worst case scenario, you get cold feet like usual but get to enjoy the wilds as usual and you've eliminated one possible solution. Best case scenario...it works and your enjoyment will increase!
If the bread bags and socks combo (make sure you also wear a liner sock) seems to work for you without introducing new issues, you may want to again consider the neoprene socks. I just find the neoprene route is much more streamlined, allowing me to use my normal shoes and have better blood flow over all.
PS: Get over the calf socks if you don't have them (as per the article, something like thin ski socks). Knee high socks put a lot less pressure on your skin, over an area where blood vessels are deeper in the leg. Around the ankle many of the blood vessels are pretty shallow (that's why many feet are veiny) so having a sock cuff in that area puts pressure points exactly where blood flow is most easily obstructed. Mid-calf or higher socks avoid this concern.