Hi Maria,
Well I would use memoQ that I believe offers 2 types of editing distance calculation and is rather user-friendly in this regard. You would need to import your strings file (create a rather simple regex text filter if needed), configure a Google MT plugin with any available API access token for this project (n.b. it will be using the basic untrained NMT model even if you plug in API token for the one that is trained), pre-translate the content with MT option on. Create a snapshot (translation version "screenshot").
Separately, have the script you created work with CGP API to translate the same set of data using the trained model. When this is done done, export a bilingual RTF from memoQ, swap the data in the right-hand side column with the translation you have in the custom-trained model translated strings file, re-import the bilingual, which will update the segments that are different from the original basic NMT model output. Create a snapshot of this version. Right-click the strings file in the project, select History/Reports, select the two snapshots while pressing CTRL, click the Calculate edit distance link. Select which measurement you are interested in (Levenshtein/fuzzy) and click Calculate.
You can also export a change-tracked Word document if you are interested in a more granular analysis.
Hope this helps.
Thanks,
Ilia Shifrin