It's been discussed in comments, I think it's worth a discussion.

First, a glance on the gains of the mod's building earnings. Assuming the empire has some Sprawl beyond the Administration Cap, one tier 1 admin building effectively gets the following per month:
1.2% of total empire Research of each type, 2% of Unity, 4% of leader upkeep Energy, 2 clerk jobs (4 amenities, 4 trade), 1 Energy + 1 Society upkeep. An easy first step into expansion.

Now a early-mid game empire. I plugged in the numbers to my 150 extra sprawl empire. 9 tier 2 buildings produce the following, each:
(4.8%) About 32 Research of each type, (8%) 18 Unity, (16%) 4.3 Energy, 3 clerk jobs (6 amenities, 6 trade), 2 Energy + 10 Society upkeep. Mostly covers some developed worlds.

An late-game empire, 480 excess Sprawl example. Tier 3 buildings, each:
(9.6%) About 250 Research of each type, (16%) 333 Unity, (32%) 18.4 Energy, 3 clerk jobs + 1 Admin (3 Unity, 14 amenities, 6 trade), 19 Energy + 60 Society. Covers most developed single-world sectors and you shouldn't need more than this.

And just for completion. Tier 4.
(19.2%) Tons of Research, (32%) Now What Unity, who cares% leader upkeep, 5 clerk jobs + 1 Admin (3 Unity, 18 amenities, 10 trade), 19 Energy + 200 Society upkeep. Covers your three-planet homeworld sector and the greedy hyperlane trolls collecting tolls.

These numbers should have clear meaning. But just to be extra clear -> In the early game with extra sprawl, they're hands-down the worst thing to build except the silo, but by mid game you should be building tier 2 on as many worlds as you need until you reach the Sprawl level and only upgrade if there are no more planets available. They're basically empire-wide self-additive multipliers that stack with all other multipliers for Research and Unity. And the larger your empire is, the larger the multiplier can get. Only they don't apply to special projects. You should know how big those Sprawl debuffs are- these buffs are equally big. With this, it is easy to completely counter the Sprawl.

SOCIETY UPKEEP: In the endgame, the extra Society-producing sources offset the upkeep a fair bit. If wisely spread across your empire, you might not even notice Society advancing any slower (perhaps even faster than Engineering). If prolific with these in early-mid-game, you might hurt yourself with those special projects, namely species altering. In the end, the Society upkeep ends up not actually being a cost, but a Research check.

UNITY UPKEEP: Suffers the same as Society upkeep. As long as it's moderated, you'll just make more Unity than the upkeep. A lot more- having a large flat cost just delays when that happens.

Goal Check: Do you want a natural feeling way to deal with spread, or do you just want to get rid of it? I like the feature, myself, but would like a way to mitigate it, perhaps eliminate for an actual cost (not a resource check).

Easy Solution: What does the game do with Every Other Empire Wide Buff? Limit 1, and it's pretty expensive. It shouldn't be able to eliminate wide Spread like this, but it is easy and doesn't break the late game.

Solution 2: Drastically reduce the Admin Cap and change upkeep to more Energy + AMENITIES. I'd recommend 5 cap to 6 energy 8 amenities, 10 cap to 14 energy 22 amenities, 20 cap to 22 energy 48 amenities, 30 cap to 30 energy 70 amenities. Perhaps crystals would be a good addition, and a bit less amenities. No limit to # on planet, so you could build a true administration world teeming with entertainment districts or just sprinkle them through the colonies. It would be as vital to the nation as the first Tech World and Capital World are, just later down the line.

This is high-intensity office work smoothing the lives of billions in multiple dimensions and environments demanding state-of-the-art fences security and monitoring systems. It identifies individuals suitable for demanding jobs to help make the most of the minds of the nation. I suggest Amenities because Administrative Cap doesn't affect it, but it directly affects productivity on that specific colony as it interferes in lives but improves the greater good. You could build one on every colony, but that many amenities will call for some additional redirected labor and building space, very seriously impacting economy and reducing specialization (except for a Resort World). At some point you might even elect NOT to reach cap in interest of more specialized economy-focused planets. Heck, maybe even keep that administrator job or two, but I think the clerks should go.

Remember, 30 cap = 9% empire-wide research that stacks with everything, even more Unity, and a noticeable bit of energy. That cap should cost something.

Still, Solution 3. Shift to starbases with imperial administration Modules, with a large energy upkeep and unity/social research cost. This is a linear progression but starbase space is in high demand. The cost here is more a choice- largely against fleet cap, trade lanes and defense.