Yes, I understand that. Parameters are within (0, Pi) which is the same as (-Pi, 0). where exactly in this region hard to say.

What is the fastest fitting method for this type of procedurally defined functions? Apparently Levenberg is not the best, too expensive. Nothing cheaper?

A little experiment.

Insert up near the top of your code

counter = 0;

Insert immediately before the last line of your Module, which returns the value of intensity,

LinkWrite[$ParentLink, SetNotebookStatusLine[FrontEnd`EvaluationNotebook[], ToString[{counter++, pw, h0, \[Sigma]0, Qw, intensity}]]];

That is going to write little messages onto the status line in the lower right corner of your window. You will be able to see the counter incrementing, the contents of your arguments to your module and the resulting intensity.

I have chosen the order of those so that the ones which will almost always have the same number of characters to be displayed each time come first. That way we can hopefully see pattern in the flood of messages.

Notice how many thousands of calls are made to your module have without any change to pw, h0 and sigma0.

In your Module in your local variable list there is b,,Qv and that worries me.

If I insert

Print[{Qw, pw, h0, \[Sigma]0, intensity}];

immediately prior to the last line of your module, where it returns the value of intensity, and run your code then there is a vast long list of lines printed which show me that your function is being evaluated for a variety of different parameters and different values of intensities are being returned. Note: you may need to kill the math kernel to get control over the machine again because of the stream of output swamping the machine.

I was hoping that seeing the parameters and result from your int function might provide a clue.

Can you use StepMonitor or EvaluationMonitor in NonlinearModelFit to observe the progress and get a better idea where it is hanging up?

Tiny probable typo:

dat3 = Import["Non-annealed data.txt", "Data"];
fitm = NonlinearModelFit[datint,...

I'm guessing datint should be dat3. True?

Any other typos if you carefully look over the files you posted?

Thanks