Plugging the numbers into different notations! Insane, right?
Juice infused Arrows = 17^592^186^44^416 (Class 5)
Juice infused Down = 17v592v186v44v416 (Class 3)
Juice infused BEAF = {17, 592, 186, 44, 416} (Class 9: Quadratic omega level)
Juice infused BAN = {17, 592 [186 \ 44] 416} (Class 16: Epsilon level)
Juice infused E = E17#592#186#44#416 (Class 7: Up-arrow notation level)
Juice infused Chain Arrows = 17 -> 592 -> 186 -> 44 -> 416 (Class 8: Linear omega level)
Juice infused Ampersand = 17[592][186][44][416] [Ampersand Notation] (Class 7: Up-arrow notation level)
Juice infused Copy = 17[592, 186, 44, 416] [Copy notation] (Class 8: Linear omega level)
Juice infused Moser = 17[592[186[44[416]]]] [Steinhaus-Moser Notation] (Class 8: Linear omega level)
Juice infused DLMAN = 17 [1 {186 (/44) 416} 2] 592 = 17 [1 {196 `44` 416} 2] 592 (Class 17: Binary phi level)
Juice infused Greek = 17A(592A(186A(44A416))) (Class 9: Quadratic omega level)
Juice infused HAN = 17(186)(44)(416)592 (Class 9: Quadratic omega level)
Juice infused H* = H*(17, 592, 186, 44, 416) (Class 7: Up-arrow notation level)
Juice infused Factorial = 17![592, 186, 44, 416] (Class 15: Iterated Cantor normal form level)
Juice infused K = K592, 186, 44, 416(17) (Class 10: Polynomial omega level)
Juice infused X = 17{186X^2 + 44X + 416}592 (Class 10: Polynomial omega level)
Juice infused Zillion = z(17, 592, 186, 44, 416) (???)
Juice infused Taro-Ackermann = A(17, 592, 186, 44, 416) (Class 10: Polynomial omega level)
Juice infused s(n) = s(1)^592 s(2)^186 s(3)^44 s(4)^416 f(17) (Class 10: Polynomial omega level)
Juice infused AAN = a*(17, 592 {186, 44} 416) (Class 13: Double exponentiated polynomial omega level)
Juice infused C = 17C592/186/44/416 (???)
Juice infused Dollars = 17$[592][186][44][416] (Class 7: Up-arrow notation level)
Juice infused -illions = 17[592, 186, 44, 416] [Extensible Illion System] (Class 8: Linear omega level)
Juice infused Quick = Q<17, 592, 186, 44, 416> (Class 10: Polynomial omega level)
Juice infused Rampant = r(17, 592, 186, 44, 416) (Class 10: Polynomial omega level)
Juice infused SAN = s(17, 592, 186, 44, 416) (Class 9: Quadratic omega level)
Juice infused UNAN = 17 [416 {186} 44] 592 (Class 12: Exponentiated polynomial omega level)
Juice infused @ = 17@592@416@186@44 (solved from right to left) (Class 8: Linear omega level)