Can I use existing dictionaries (American Heritage, Merriam Webster) to compile my own derivative dictionary?

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The copyright that attaches to dictionaries is quite thin --- but it nonetheless exists and protects the publisher's selection of words, the particular way the definitions of those words are phrased, and the supplemental information provided such as the words' etymology, slang applications, and usage examples.

I think you would be teetering on the edge of infringement -- if not falling over -- if you take 2 dictionaries, copy their word lists, and paraphrase their definitions into a consolidated "new" dictionary. The publishers of those dictionaries would likely object.

If the raw material for your dictionary was 50 dictionaries, however, and you exercised creativity in selecting the particular words and crafting your version of the words' definitions and added your own supplemental information then the publishers of those dictionaries would have no complaint.

These comments are made for educational purposes only and do not constitute legal advice. No attorney-client relationship exists between us.

If you truly follow the protocol you described, you should be safe. Your work can't look like any of your competitor sources. Obviously, the word list would be very similar, but your interpretation, analysis, and visual presentation must different.