I have been using Noteworthy Composer (NWC) for several years, and I've recently looked at some of Finale's capabilities. Some of what I write here is relevant to music transcription in general but not necessarily to submission of material to Mel Bay.

NWC is quite acceptable for the entry of melodies and lyrics, but it has limitations on the entry of chords. In NWC, chord names appearing above the staff are only text fields; they do not transpose when the melody is transposed, and there is no special font that matches lead sheet conventions for chord names. An add-on program called "Noterow Assistant" was once available in beta test mode, providing both a chord name font and a fretboard grid font; strangely, the help page for this program is still available
here, although the program is not. However, if you can find any other TrueType chord-name-friendly font, you can specify that NWC use it for chord names.

Compared to other entry-level notation programs available at the time I selected it, one advantage of NWC was that it could output the notation as a Windows Metafile graphic image. This is better than a bitmap image (such as .gif or .tif), which is in turn better than a screen capture, which in turn is better than nothing, because the metafile is scalable: as you enlarge the image, your notes and text do not develop "jaggies". If you enlarge the image enough, you may notice that the note heads and stems do not align exactly, but I have only rarely needed such enlargements. Also, if you shrink the image, Windows uses font hints to make the text look as good as possible at the point size you're using. Therefore, the graphic output from NWC is optimal for pasting into word processing documents, allowing you to notate one verse of a song and to enter the remaining verses and any supplementary comments as ordinary text. I was surprised, when recently helping a friend with Finale (one of the higher-end versions, I'm not sure which one), to find that it did not have the ability to similarly export its notation to any convenient graphics format.

I agree that the optimal strategy is to enter notation using whatever program a publisher will eventually want to use to prepare the final copy for printing. However, the alternative is not simply to print hardcopy pages for someone to re-key into different software. Almost any notation program can export and import MIDI files, which will save some of the work of re-transcription. Depending on the programs, it might be necessary to make minor adjustments such as filling out the first measure to the full number of beats instead of leaving it as just a pickup note. Also, there is a not-very-expensive program called Harmony Assistant that claims to be able to import and export native notation files from NWC, Finale, Encore, and a few others, as well as handling ABC notation and MIDI. You might be able to use this either for conversion between two other programs or for original note entry prior to final formatting by another program.