Evaluating and Plotting 3F2 is very slow

Question

I am interested in certain hypergeometric functions $ G_p(z) = \frac{1}{2} {}_3F_2 \left( \begin{matrix} p & p + 1 & \frac{1}{2} \\ 1 + i & 1 - i & \end{matrix} ;z \right) $ and would like to plot them in the complex $z$ plane, on both sides of the branch cut $\operatorname{Re} z \in (1,\infty)$. However

G[p_, z_] := 1/2 HypergeometricPFQ[{-p, p + 1, 1/2}, {I + 1, -I + 1}, z]
ComplexPlot[G[1/2, z], {z, -I, 2 + I}, PerformanceGoal -> "Speed", ColorFunction -> "GreenPinkTones"]

takes at least 5 minutes to evaluate. (I ran it inside TimeConstrained.) I thought maybe this is just because there is a lot of detail for ComplexPlot to resolve. (Actually, I'd like the plot with ColorFunction -> "CyclicReImLogAbs", which would be even more computationally intensive in that case. And eventually with PerformanceGoal -> "Quality", too.) I tried evaluating the function on a fixed grid to see if that excessive detail was the problem:

mesh = Flatten@Table[{x + I y}, {x, -1, 1, 0.1}, {y, -1, 1, 0.1}];
AbsoluteTiming@G[1/2, mesh]/Length@mesh
(* 0481893 *)

≈ 50 ms per function evaluation, no wonder plotting it is slow!

In contrast, evaluating and plotting ${}_2F_1$ is reasonably fast:

H = Hypergeometric2F1[-9/14, 1, -2/3, #] & ;
EchoTiming@ComplexPlot[H[z], {z, -I, 2 + I}, PerformanceGoal -> "Speed",
 ColorFunction -> "GreenPinkTones"
 ]
(* 0.876022 *)
EchoTiming@ComplexPlot[H[z], {z, -I, 2 + I}, PerformanceGoal -> "Speed",
 ColorFunction -> "CyclicReImLogAbs"
]
(* 2.98155 *)
First@AbsoluteTiming@H[mesh]/Length@mesh
 (* 0.0000524331 *)

As seen on the last line, ${}_2F_1$ is roughly $1000$ times faster to evaluate than ${}_3F_2$! I saw elsewhere on MMA.SE that MeijerGReduce could offer speedups, but it didn't work in this case.

Is this because higher hypergeometric functions are inherently expensive to compute? Is it a known issue? Is there anything I can do to speed the computations up?

I am on Linux, Mathematica 13.0, i9-10900K @ 3.70 GHz. The machine scores 4.49 on the WolframMark Benchmark.