Apology in advance - this is long.
Like almost everything else in Elvenar, I find the answer to this varies based on what kind of FS it is, and what the FA goals are.
My goal with every FA is to give the members the knowledge and tools, to be able to balance their own production. If players make approximately the same number of each badge over the course of the FA, they will have an easier time donating their badges. I know some FS's tell their members exactly what to make and when to make it, but I really, really don't like micromanaging players. I feel like that's a recipe for making the FA stressful for everyone, and with the crappy prizes it should at least be fun.
For small FS's (either small in member number, or FS's full of of newer players) where it can be a struggle to get through the maps, I like using countdown threads for the long production badges. The countdowns serve as more of an educational tool so players have a sense of how many of each badge will be needed and helps to ingrain the badge requirements. It gets them thinking in terms of the sets that are needed to produce badges. They are highly inaccurate though, given that you will never have 100% of members using them, the math can be a bit tricky for new players if you ask for the count as the badges are started, and doesn't help if players dump those badges into waypoints you aren't completing. This puts the highest demand on the players of anything I use, but it can provide a rough structure to help get over the initial hump of getting all the prizes, and eventually clearing all the maps, since everyone can see where you're deficient.
The next tier are FS's looking to be more competitive, but not vying for the top spots. These are FS's that clear all (or almost all) of all 3 maps and spend a decent amount of time in the pit. For those, I favor semi-directed production and inventory calls. Semi-directed means I post daily status updates with recommendations/reminders about what to produce. My goal here is to teach how to balance. Most players don't think about things like 4 T1's can make 2 statues or 2 necklaces every 2 days, or 10 workshops can make 2 smiths, or 2 farmers and a carpenter every day. Understanding that is the key to balanced badge production. Inventory calls can include requesting an initial report of what members have built (i.e. how many added T1's and workshops), and then either daily or occasional reporting of badge inventory. I find daily to be overkill, and usually reserve requests for when we enter the pit and then maybe once again with a day or 2 to go. It's really just to check that we don't have an overload of any one badge type. Often players in these FS's like a bit of handholding of the "Just tell me what to make and I'll make it" variety, or there may be a number of members who aren't able to play frequently and need to focus 1 and 2 day badges, so this can help you manage shifting productions, or organize a pit party to help pull badges from the time limited players, if there is an obvious imbalance. This is also highly inaccurate given the reasons
@crackie stated above, but I accept and am comfortable with that.
For the highly competitive FS, I'm in total agreement with
@crackie that tracking isn't necessary. Getting together 25 crazy people is what you need, lol.
Regardless, I always run a private spreadsheet. I track initial builds (I don't ask for these, I just use elvenarchitect to get the numbers) and badges placed on the maps. If I'm doing inventory calls, I track those as well. My tracking doesn't really determine the FS's success though. It's all about communication, encouraging balanced production, and ultimately, individual player commitment.