Optimizing a series expansion for high order in $x$

I would like to expand the following function at $x sim 0$ up to some high $x_text{max} = Delta_text{max}$:

$$16 sum_{Delta=1}^{Delta_text{max}} sum_{s=0}^{Delta-2} f_{Delta,s} frac{(s+Delta)(1+s-Delta)}{(s-Delta)(1+s+Delta)} _2F_1 left(frac{1}{2},-s,frac{1}{2}-s,1right) _2F_1 left(frac{1}{2},2+Delta,frac{5}{2}+Delta,x^2 right) x^{2+Delta}, tag{1}$$

where $f_{Delta,s}$ are numerical coefficients. The series expansion should be performed after doing the following replacement (everywhere except in the subscript of $f_{Delta,s}$ and in the summation limits):

$$Delta to Delta + g^2 Delta^{(2)}_{Delta,s} + g^4 Delta^{(4)}_{Delta,s}, tag{2}$$

and expanding in $g$. Again the $Delta^{(k)}$ are numbers, which depend on $Delta$ and $s$. I am not interested in $log$ terms, which can be discarded by setting the rule $log x to 0$.

So far I wrote the following simple code:

Δmax=5;
ℒ0s2 = 1/((s - Δ) (1 + s + Δ)) 16 x^(2 + Δ) (1 + s - Δ) (s + Δ) Hypergeometric2F1[1/2, -s, 1/2 - s, 1] Hypergeometric2F1[1/2, 2 + Δ, 5/2 + Δ, x^2]
Sum[Series[(f[Δ, s] Series[ℒ0s2 /. {Δ -> 
Δ + g^2 Δ2[Δ, s] + g^4 Δ4[Δ, s]}, {g, 0, 4}] /. {Log[x] -> 0} // Normal) /. {Δ -> ΔΔ, s -> ss}, {x, 0, Δmax}] /. _?(N[#] == 0 &) :> 0 // Normal, {ΔΔ, 2, Δmax}, {ss, 0, ΔΔ - 2}]

Unfortunately this is insanely inefficient for high $Delta_text{max}$. For $Delta_text{max}=5$ the computation takes less than a second, for $Delta_text{max}=10$ about $20$ seconds, for $Delta_text{max}=15$ it took $3$ minutes,… I let it run the whole night yesterday to reach my goal, which is at least $Delta_text{max}=60$, and it was still running this morning!

Any suggestion how this expansion could be done (much) faster?