Generalizing technique to handle General::munfl error?

Question

In contrast to earlier versions of Mathematica, in versions 11.3 and later Mathematica no longer switches to arbitrary precision when it detects a MachineNumber underflow. While this behavior is consistent with IEEE 754, this can also be problematic.

Background (and a workaround for the exponential function can be found here: New General::munfl error and loss of precision However, since functions other than exponentials can cause underflows, a more general workaround is useful. I am trying to use the method proposed in the second solution of: Underflow error General::munfl from E^x instead of Exp[x]

However, the trappedEvaluation function defined there is failing to detect or fix the underflow in the following:

(* This is the function from the above-mentioned solution *)
SetAttributes[trappedEvaluation, HoldAll]
trappedEvaluation[expr_] := Check[
   expr, 
   numericize@Block[{Real}, 
       f_?nfQ[a___, r_Real, b___] ^:= Rationalize[Unevaluated@f[a, r, b], 0];
       expr
   ], 
   General::munfl
 ]
nfQ = SystemDumpHeldNumericFunctionQ;
numericize[e_] :=  With[{res = N[e, 16]}, 
     Quiet@Check[
        N[res], 
        res, 
        General::munfl
     ]
  ]
(* Here is my function: )
 f[x_] = Exp[-(1/x)]WhittakerW[-(I/x), 1/4, I*x];
(* Test: *)
 trappedEvaluation[f[.0001]]

This still returns 0.+0.i. In fact, based on the analytic expansions in the DLMF this should grow exponentially as x approaches 0, and the behavior up until the underflow error is consistent with this.

Ultimately, I need to make a log plot of f[x]*Conjugate[f[x]], and f'[x]*Conjugate[f'[x]] so the solution has be able to work at the arbitrary points that Mathematica chooses when plotting. Therefore rationalizing by hand (or setting the precision by hand) isn't a solution. I'm afraid the derivative will also cause issues, but first I want to get it working on my function.

I don't believe the problem is in my implementation of trappedEvaluation, as it works appropriately on the function in Underflow error General::munfl from E^x instead of Exp[x]. Namely,

   sigma = 0.01;
   gaussian = Function[x, 1/(Sqrt[2 Pi] sigma) Exp[-1/2 (x/sigma)^2]]
   gaussianP[x_] = D[gaussian[x], x]
   trappedEvaluation[gaussianP[1.5]]

returns -9.206189566469410*10^-4881 as it should. I would much appreciate it if someone could help me understand how to generalizing the trappedEvaluation function appropriately.