Help to try and make my code finish running. Series of incomplete elliptic integrals

I have the following code

ord = 2;
Roo = AsymptoticSolve[h - q^3 (q - 2) == 0, q, {h, 0, ord}];
aexp = Roo[[4]][[1]][[2]];
bexp = Roo[[2]][[1]][[2]];
cexp = Roo[[1]][[1]][[2]];
dexp = Roo[[3]][[1]][[2]];
b1exp = Re[ComplexExpand[cexp]] // Simplify;
a12exp = Im[ComplexExpand[cexp]]^2 // Simplify;
A2exp = Assuming[h > 0, 
    Series[(aexp - b1exp)^2 + a12exp, {h, 0, ord}]] // Simplify;
B2exp = Assuming[h > 0, 
    Series[(bexp - b1exp)^2 + a12exp, {h, 0, ord}]] // Simplify;
gexp = Series[1/Sqrt[Sqrt[A2exp*B2exp]], {h, 0, ord}];
k2exp = Series[((aexp - bexp)^2 - (Sqrt[A2exp] - 
         Sqrt[B2exp])^2)/(4 Sqrt[A2exp*B2exp]), {h, 0, ord}];
y0 = Series[
   Solve[q^3 (q - 2) - (h - (1/\[Epsilon])^2) == 0, 
       q][[3]][[1]][[2]], {h, 0, 2}, 
   Assumptions -> \[Epsilon] != 0] /. {\[Epsilon] -> 10};
ExpCos\[Phi] = 
  Series[((aexp - Normal[y0])*Sqrt[B2exp] - (Normal[y0] - bexp)*
       Sqrt[A2exp])/((aexp - Normal[y0])*
       Sqrt[B2exp] + (Normal[y0] - bexp)*Sqrt[A2exp]), {h, 0, 1}];
Exp\[Phi] = 
  Pi + Assuming[h > 0, 
    Series[ArcTan[
      Sqrt[(1 - (Normal[ExpCos\[Phi]])^2)]/(Normal[
         ExpCos\[Phi]])], {h, 0, 1}]];
Collect[Normal[
  Assuming[h > 0, 
   Series[Normal[gexp]*
     Normal[Series[EllipticF[Exp\[Phi], k2exp], {h, 0, ord}]], {h, 0, 
     1}]]], h]

The goal is to obtain the final series expansion, so I can analyze it. The problem is the series expansion Exp\[Phi] does not finish running, at least after a couple of hours. I am wondering if there is anything I can do to optimize my code, and to actually make this finish running? In case anyone is interested, this is related to the series expansion of incomplete elliptic integrals of first kind.

Thanks in advance.