I have to express first that without taking a detailed look at you, it is hard to sift through all of the potential variables and contributors to your symptoms. Any advice I give you is limited by this fact. There is no substitute for having a skilled physiotherapist look at you. It is possible your big toe pain is referred down from your anterior tibialis muscle, or even a nerve (like your deep peroneal nerve). I suspect it is more likely that it is the MTP joint (or the knuckle joint) of your toe. The stretch you’re describing puts a lot of pressure on that joint, perhaps a lot more than when you manually push on it.
If it is the 1st MTP joint, it would often be a big thickened around the joint line (a bit swollen and perhaps the bones being a bit more prominent), a bit tender around the joint line, and perhaps bent in towards your 2nd toe. If you have none of these things, it doesn’t rule out a MTP problem, but it may indicate something else happening.
A problem like gout can’t be ruled out either, although the flare ups are often more related to eating and drinking habits.
You are on the right track to work on the mobility of your ankle and leg. There may be a few more factors involved, like the strength and control of the muscles that operate around your foot- especially your ‘intrinsic’ muscles of your foot and the muscles that twist your foot in and out. Physiotherapy prevailing wisdom has moved on a little from looking at foot posture (as in flat foot vs. high arch) as the key to foot problems. Many people with high and low arches have no problems. With all that, if you have a high arch, it may make it more likely for your mid-foot to be stiff, for your big toe to have mobility forced upon it, and for you to get tight down the outside of your lower leg. You can’t change your posture, but the right combination of working on your whole leg strength and control, using strategies like appropriate rest, footwear, strapping or taping of your foot, or orthotics to even the load through your foot could give you some relief. Very often, you compensate due to the pain and that asymmetry with your movement can perpetuate the problem.
I would suggest you seek a physiotherapist out to work out what you need. There is a good chance you can get this settled down and return to normal activity.