As Michael indicates, a "print" on screen is not really an accurate depiction of a real print out.
Here's a possible idea though, in photoshop/gimp you can do a 200% enlargement using Bicubic Smoother (best for enlargement) to attain an interpolated uprezzed image.
You will need to do a clarity/contrast/curves/saturation/sharpening on this uprezzed image to get it in shape for printing.
Send this uprezzed file to snapfish and print out at 19x29
and also send them the original file, and have them print out the original file at 15x10.
When you get both back, see if the 200% uprezzed version meets the same level of image quality as does the original file sized print out, if the 200% printout does/or does not, then you have some benchmark for future printing needs.
Incidentally, does snapfish provide you with an ICC profile for their print processing? If they do, you can use that to soft proof and make corrections before actually sending them the file(s) for printing.