Just a few points off the top of my head:
My main question is what do other cyclists use for a cooking system that travel like myself?
What you cook with is really driven by what you want to cook...and vice-versa.
Starting to plan my Trans-Am trip next May East to West in 2022.
Oooo! Lots of time to experiment and practice, then, developing favorite recipes, menus and your cookcraft.
Cookbooks: In another thread I praised the old classic
Cooking on the Road by John Rakowski, sometimes available used on Amazon or at your local used book store. In current print,
Bike.Camp.Cook. by Tara Alan is good. Don Jacobson's
The One Pan Gourmet pursues the interesting idea of minimizing your kitchen tackle by optimizing your recipes.
Stoves: For 30+ years I relied on my Coleman 400A white gas stove. Huge power but with a finely controlled, gentle simmer. It had a very broad, wind resistant burner that was neither prone to causing hot spots in the pan nor scorching the food. It burned pump gasoline - the world's most common fuel - just fine. Loved that stove. Back in the day my buddies with Svea 123s were in awe of the Coleman. Alas, much like some cycletourists, it got cantankerous in its later years. I took it apart to clean it and it hasn't worked since. It's been decades since Coleman made the 400A, and years and years since they offered repair parts. Yeah, yeah, you can still get parts for Svea 123s. Whatever.
As HBC mentioned, in some forest/campgrounds alcohol and wood stoves are banned by regulation. Conversely, the only stove you can count on flying with is an alcohol burner like the Trangia - and at present you can fly with the fuel, too! Ha, take that, TSA! I used my Trangia exclusively for several years. I loved its silence, dead simple operation and stone-cold reliability. You're not really carbon neutral if you use bio-alcohol, but you can pretend you are. You can spill a little fuel without extinguishing all life in the soil. Plus, the Trangia has a screw top lid and, well, something of a simmer ring. I've never had any trouble being flush with alcohol fuel. Downsides? Well, it's not terribly powerful and the simmer is pretty primitive.
I've taken my Expedition Research solid fuel (hexamethylenetetramine) stove along for 'backup'; never
had to use it but played with it some. What can I say about it? Hmm. Well, it makes heat after a fashion and it's extraordinarily lightweight.
I agree with cycle cookbook authors Rakowski and Alan: if you want to
cook-cook, use a gas (liquid or gaseous) stove; one with a good simmer and preferably a broad burner head. Not owning any equipment and feeling haute bourgeoisie, today I'd probably get an all singing, all dancing Optimus Polaris Optifuel. With a, ahem, modest budget and a box full of old equipment, these days I mostly camp-cook with a plebeian Coleman Peak 1 single burner isobutane stove. I guess if I mis-planned/under budgeted/was unlucky with the isobutane canister supply, I could get by for a meal or two with the hexamethylenetetramine.
If one goes in for the 'skillet' school of One Pan Gourmet, I like the GSI Pinnacle. For the 'pot' school, the MSR Alpine Stowaways are nice. On tour about 40 years ago, I found an Opinel carbon steel #8 and I've carried it on tour ever since. I like how easy it is to keep razor sharp, its locking blade and the chunky, easy to grip handle. Buying new, though, I'd get the smaller #6.
I love the thermodynamic excellence of our OP's MSR Windburner. However, comparative tests suggest the Windburner does not simmer well, and its system-integrated pot is relatively tall and slender. Recipes will need to be chosen/developed accordingly.
BTW, our hosts here on this forum, Adventure Cycling, featured a blog post last month on the joys of wood fires. I guess I camped in too many sites that had been absolutely denuded by earlier guests, subscribe too much to 'leave no trace' and breathed too much wood smoke from poorly built fires in the next campsite over to really be a fan. The Trump Administration's EPA declared burning wood was carbon neutral, so it's got that going for it, but others have countered that depends on many assumptions that are seldom met.