It doesn't sound like any of these were the cause of the rosacea. I have that too, on the bridge of my nose. It used to be more noticeable when I drank, but as I got older, it became just a constant thing. I have some medication which is mostly ineffective.
I tried a dermatologist, a nutritionist and a kinesiologist. Dermatologist said, "I have a medication which will fix it but you won't like the side effects." The kinesiologist was a genius & true miracle worker for several issues my family had (that story another time) but he couldn't fix the rosacea (RIP
Dr Caskey). The nutritionist told me "Within a couple months, we'll find what triggers the rosacea." Eight months into it, it started getting better, but then got worse. So I suggested we stop suspecting foods and try environmental factors (mold, dust, dander, pollen, etc). We tried a number of those and, just like certain foods, certain environmental factors made it worse, but aren't the root cause.
Eventually I got an eye sty and was told by my eye doctor it's related to the rosacea. Left untreated, it could cause serious vision problems. So I relented and started taking Doxycycline and it works well.
On a scale of 1-10 (1 = clear skin, 10 = people asking if I have windburn):
From late 2005 (when it exploded) to 2015 (start of elimination diet): varying between 6-10
During strict elimination diet 2015/2016: between 5-8
Learning to moderate it based on known triggers: between 4-7
While on Doxy: between 2-3
Stopping Doxy: between 4-6
What I want, and am still searching for, is a cure. Doxy sometimes gives me an upset stomach (like it did this morning). The instructions are "take without food ... unless you get a stomach upset, then take it with food (but it will be less effective)." I don't like the idea of putting this stuff in my body for the rest of my life.