I am pretty sure you are correct; leaky valve stems and bad bead sealing are what causes most tire failures. Fix-a-Flat not only DOES NOT work, but when you take your tire in to get it worked on, they charge you $10 a tire to scrape it back out. Therefore it is best to save the money on the useless can, and money at the tire repair shop, and just not use it.
The key to happy tires on a farm are tubes. Trust me on this, I know this reality well and am not steering you wrong (pun intended).
Whether slamming into rocks in a field that bends the rim, or squatting out when getting a huge load of manure; tires on a farm take some serious abuse. Tubes are nice because they are far more forgiving. Other then being careful not to pinch the tube when remounting the tire, you will be done with your tire repair job by the time you could even figure out where the leak is on a tubeless tire. It is also a lot safer then using WD-40 or starting fluid on tires to get them to seal on the bead too!
If you use calcium cloride for added weight, you will want tubes anyway, and tubes are easy to repair. You can buy a tube patch kit at an autoparts store for $3 and patch 6 punctures with it. When you first do it you will be amazed; how on the earth can something so fast, easy and cheap and still work? I timed it one day and I was able to pull the front tire off my Kubota, break the tire down, pull out the tube, clean the puncture hole, patch it, reseat the tire, and get it back on the
tractor in less then 20 minutes. I think the silly thing had 3 patches on it, but had I bought a new tube, it would have only been $16 dollars. A tube for the rear tire on my tractor...$56.
Naturally you will want a good valve core tool that not only inserts the core, but can clean out the threads too. I think mine cost $3 bucks, and I always have spare valve seat cores just in case one needs to be replaced. Another cheap thing to have on hand is an air chuck as they seem to go bad when you need them the most. If you are adding this all up, you can see the cost for having a good repair kit kicking around is less than $20, or put another way, a lot less then what a tire repair shop will charge you for (1) tire fix.
Tubes man...tubes!