performance tuning - ParallelTable behaves differently when it is run inside a package

I've been butting my head against some very weird behaviour by ParallelTable, and its interaction with packages, over the past few weeks, and making relatively little headway towards even reproducing the weird behaviour in a stable way. I just managed to crystallize some of this behaviour in a clean format and I would like some help understanding what's going on.

Consider, as an example of a relatively heavy calculation that one might want to parallelize, the following sum:

AbsoluteTiming[
Table[

  Sum[
   BesselJ[0, 10^-9 k]/(n + 1.6^k), {k, 0, 10000}
   ]
  , {n, 0, 12}]
]

(* {5.67253, {etc.}} *)

If I parallelize this, even for something this small, it gets faster:

AbsoluteTiming[

ParallelTable[
  Sum[
   BesselJ[0, 10^-9 k]/(n + 1.5^k), {k, 0, 10000}
   ]
  , {n, 0, 12}]
]

(* {1.89187, {etc.}} *)

(Minor change in the denominator to avoid what looks like caching.) OK, so far so good. Now, suppose I wish to make this calculation into part of a package, which might look like this:

BeginPackage["package`"];
function::usage = "function[x] is a function to calculate stuff";
RunInParallel::usage = "RunInParallel is an option for function which determines whether it runs in parallel or not.";
Begin["Private`"];

Options[function] = {RunInParallel -> False};

function[x_, OptionsPattern[]] := Block[{TableCommand, SumCommand},
  Which[
   OptionValue[RunInParallel] === False,

    TableCommand = Table; SumCommand = Sum;,
   OptionValue[RunInParallel] === True,
   TableCommand = ParallelTable; SumCommand = Sum;,
   True, TableCommand = OptionValue[RunInParallel][[1]]; 
   SumCommand = OptionValue[RunInParallel][[2]];
   ];
  TableCommand[
   SumCommand[
    BesselJ[0, 10^-9 k]/(n + x^k), {k, 0, 50000}
    ]

   , {n, 0, 12}]
  ]

End[];
EndPackage[];

In particular, I have given it the option RunInParallel to decide whether to use a normal Table or a parallelized one. If I run it like this, however, I get much worse timings:

AbsoluteTiming[function[1.1, RunInParallel -> True]]
AbsoluteTiming[function[1.2, RunInParallel -> False]]


(* {31.465, {etc.}} *)
(* {34.5198, {etc.}} *)

Note here that (i) both versions are much slower than their non-packaged cousins, and (ii) all the speedup from the parallelization is gone.

To try and probe this a bit further, I tried to add some functionality to let me extract the calculation and then run it separately. That is, running

function[1.3, RunInParallel -> {Inactive[ParallelTable], Inactive[Sum]}]]

returns the calculation that it would have run, but with the Table and Sum wrapped in Inactive statements:

Inactive[ParallelTable][
 Inactive[Sum][

  BesselJ[0, Private`k/1000000000]/(1.3^Private`k + Private`n)
 , {Private`k, 0, 50000}]
, {Private`n, 0, 12}]

I can then simply pop them open with a corresponding Activate statement. However, when I do this,

AbsoluteTiming[Activate[function[1.9, RunInParallel -> {Inactive[ParallelTable], Inactive[Sum]}]]]
AbsoluteTiming[Activate[function[1.8, RunInParallel -> {Inactive[Table], Inactive[Sum]}]]]

(* {11.7112, {etc.}} *)
(* {35.7969, {etc.}} *)

the timings come out as something else entirely, yet again. I'm a bit baffled about why the calculation is slower through the package than outside it, but mostly it's the parallelization that bothers me: why isn't the in-package parallelization able to work as well as the Activate[Inactive] route? Why was the parallelization lost in the first place? Did I fall into a bug or something?

Any help in understanding this will be welcome.

(All of this run, by the way, on a 4-core 4-thread Intel Core i5-2500 with 4GB RAM, MM v10.4 over Ubuntu 15.10.)