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My first price suggestion, here we go :D
There are 2 in existence of this hat, the other one hasn't moved in 5 years.
Item history: https://backpack.tf/item/3339540509
1st sale: 90 keys pure
https://backpack.tf/profiles/76561198140316312#!/compare/1630713600/1630800000
https://backpack.tf/profiles/76561199087332329#!/compare/1630627200/1630800000
2nd sale: 90 keys pure
https://backpack.tf/profiles/76561199087332329#!/compare/1634169600/1634256000
https://backpack.tf/profiles/76561198025018960#!/compare/1634169600/1634256000
3rd sale: 94 keys in items: Cirlcling Heart Brotherhood of Arms (63 keys) + Spectral Spectrum B.M.O.C. (20 keys) + Exorcism Strange Spec. Ks. Scattergun (5 keys) + Exorcism Strange Spec. Ks. Eyelander (6 keys)
https://backpack.tf/profiles/76561198025018960#!/compare/1635033600/1635379200
https://backpack.tf/profiles/76561198984595114#!/compare/1635120000/1635465600
4th sale: ~100 keys in items: Duped Exorcism Prof. Ks. Australium Rocket Launcher (Team Shine + Cerebral Discharge)
https://backpack.tf/profiles/76561198984595114#!/compare/1635465600/1635984000
https://backpack.tf/profiles/76561198292137994#!/compare/1635465600/1635552000
5th sale: 120 keys pure
https://backpack.tf/profiles/76561198292137994#!/compare/1636675200/1636761600
https://backpack.tf/profiles/76561198431089224#!/compare/1636675200/1636761600
6th sale: 63 keys (quicksell)
https://backpack.tf/profiles/76561198431089224#!/compare/1637452800/1637539200
https://backpack.tf/profiles/76561198164651434#!/compare/1637452800/1637539200 (not visible in inventory as buyer traded the hat to their trading bot on the same day)
7th sale: 100 keys pure
https://backpack.tf/profiles/76561199101711836#!/compare/1637539200/1637625600
https://backpack.tf/profiles/76561198043501673#!/compare/1637625600/1637712000
8th sale: ~100 keys: Paid item overpay for my Green Energy Whirly Warrior:
Burning Flames Flamboyant Flamenco (380 keys) + Genuine Prof. Ks. Original (15 keys) + Hot Prof. Ks Horror Holiday Flame Thrower (30-35 keys) + Frostbite Full Metal Drill Hat == Green Energy Whirly Warrior (400 keys)
https://backpack.tf/profiles/76561198043501673#!/compare/1637712000/1639094400
https://backpack.tf/profiles/76561198080594357#!/compare/1638921600/1639094400
9th sale: 180 keys pure
https://backpack.tf/profiles/76561198080594357#!/compare/1642377600/1642464000
https://backpack.tf/profiles/76561198119161228#!/compare/1642377600/1642464000
One quicksell at 63 keys, 3 sales around 90 keys, 3 sales at 100 keys, one at 120 keys, and the latest sale at 180 keys.
Given that the lower sales are the older ones, I'm confident to include the last (possibly outlier) sale too in the price range. Going with 90 - 180 keys
1: Not sure where you're getting the values for some of these items (such as the spells): you need to provide a mini for each spelled item you're using.
2: If the values are correct: 90-180 is way too big of a range. I'd personally go with 90-120 here, as 180 is way out of line with the rest of the sales.
3: sale 8 shouldn't be used to price the full metal drill hat (but it's not a sale that changes anything in your sugg).
Sales 1 and 2 are too old to use, as they're each over 3 months old. The Brotherhood of Arms in sale 3 is outdated, so you'll need to update its price first. Additionally, you'll need to supply sales to support the valuation for the spelled items in sales 3 and 4.
If the buyer in sale 5 paid 120 Keys to dump it for 63 Keys in sale 6, neither of those sales should be used, given the massive difference.
Sale 8 is a bulk sale, as the item you're pricing is worth less than 50% of the trade's value, so that can't be used either.
As Cedar mentioned, with almost every sale at or below 120 Keys, 180 looks to be too high.
Once you are able to find sales for the Brotherhood and spelled items, you could make a range using sales 3, 4, and 7.
Until you find sales, this suggestion will need to be closed.