Replace the output of a module containing local variables by their actual value

Question

I want to construct a function as the output of a Module, but I obtain the local variables as part of the output. This is a problem when I try to construct many of these functions in a parallel table, because all these local variables appear to die when the parallel computations end.

Minimal example:

If I write

Module[{i = RandomInteger[{0, 100}]},
 Function[x, x + i]
 ]

I obtain

Function[x$, x$ + i$197286]

Now the problem:

If I write

t = ParallelTable[
  Module[{i = RandomInteger[{0, 100}]},
   Function[x, x + i]
   ],
  4
  ];

Through[t[5]]

I obtain

{5 + i$19726, 5 + i$21792, 5 + i$20597, 5 + i$19520}

and the variables like i$19724 have no value.

If I use Table instead of ParallelTable I get what I want

{60, 13, 62, 13}

I found a workaround by doing

Module[{i = RandomInteger[{0, 100}]},
 With[{ei = i}, Function[x, x + ei]]
 ]

obtaining

Function[x$, x$ + 15]

which is EXACTLY what I want. I prefer to have concrete values inside the functions, even if I don't use parallelization.

But I have to introduce a new variable. And this is a problem if there are many of these constants inside the function. Is there a way to solve this problem without using a new variable?