Sorry if I wasn't clear.
You (and your fellows) each place 1 (and only 1) of these buildings months ahead of a FA. It costs each player 4x4 of space that would have been otherwise be used for other purposes (maybe with not-very-significant nominal culture or pop provided). Every production, be it Beverage or Toolbox, Figurine to Bed, when completed, 00% goes to your normal inventory, 1% goes to the FA pool. It costs you 1% of your overall production for months. During the 3 maps of the Fellowship Adventure, the same thing continues. You get the normal badge cred50 Beverages to make a Brewers Badge, but you are still being taxed 1% of your production to the FA pool, with only 99% of the suppplies from those Beverages going into your personal inventory. Once you get to the Endless Pit, the Archmage of the Fellowship may spend the quantities in the pool to make items that would count towards badges for the Pit. This would use up Supplies, Planks, Steel or Marble. Normal Fellowship badge production, you produce 50 Beverages, you keep the supplies AND you gain the badge. Using the FA Pool, if the Archmage makes a Brewer Badge for the Pit, he is trading the collected supplies for the badge. Spending the supplies. You've already received the 3 map rewards. The only thing you're fighting over is the ranking of your Fellowship in the Tourney, and the minor amount of bonus that you get in the top 100. And lastly, unused at the end of the Tourney are split back to the fellows. Originally, I didn't think this would be destabilizing or unfair, since I figured that the Fellowship could always have traded that themselves, but I hadn't considered that there currently is no way to trade Supplies, or that there are Supply limits. So, maybe unused resource are simply thrown out after the Tourney ends.
Yes, it's different then what currently happens. Wouldn't be much of a suggestion if it was restating existing mechanics.
Yes, it would help a strong Fellowship with a fully active roster. Sounds like an incentive to have a strong and active Fellowship.