Should I use "got" or "gotten" in the following sentence?

Solution 1:

This article (emphasis mine) would be hard to improve on:

As past participles of get, got and gotten both date back to Middle English. The form gotten is not used in British English but is very common in North American English, though even there it is often regarded as non-standard.

In North American English, got and gotten are not identical in use. Gotten usually implies the [punctive act /] process of obtaining something, as in he had gotten us tickets for the show, while got implies the state [durative] of possession or ownership, as in I haven’t got any money.

[Oxford Dictionaries]

An American might well prefer 'gotten' in the OP; a Brit would probably not, and might well not like the sound of the 'got' version either, choosing to rephrase, as Preetie suggests.

Solution 2:

per The Cambridge Encyclopedia of the English Language (p.311):

"Gotten is probably the most distinctive of all the AmE/BrE grammatical differences, but British people who try to use it often get it wrong."

Gotten is much more common in AmE.

I like the sound of your use of 'gotten' in that sentence. "...had been lost" sounds so passive, whereas "...had gotten lost" sounds more tragic.

"The child had been lost on the highway." "The child had gotten lost on the highway."

Which has more impact?

Solution 3:

In the example given, I would use "gotten." But that's only if you think the word "gotten" has a place in our language. To me, there is a legitimate and useful difference between "got" and "gotten." To say you've "got" something means that you have it, now. To say that you've "gotten" something means that you've obtained or received it in the past. The example given doesn't use "got/gotten" in that way, but given the continued use of the two words in American English, "had gotten lost" sounds better to my ear than "had got lost." It's more a matter of consistency than of correctness.