PDF version (solution is on the second page)
Back when I did most of my constructing on paper, I would start with a word or two, and then try to work out from there which empty boxes needed consonants and which needed vowels. Say for example that I had the word LUNCH across the top left corner, and I wanted to stick another 5-letter word under that. Not many words start with L followed by another consonant, so it's best that this second word start with a vowel. Similarly the 3rd and 5th letters should be vowels. The 4th letter could be an H or an R or something like that. So we're looking at a v-c-v-c-v pattern. A word like ADORE might work, or even AMAZE, and we could cross that Z with CZAR or CZECH, and cross the M with UMA or UM NO. Etc.
This strategy has served me well in the past, so over the past week, I have been compiling a database of every 3-letter, 4-letter, and 5-letter word I could think of, and organizing them based on consonant/vowel pattern. I'm up to 3900 words right now. Obsessive? A little bit, yes.
Anyways, come back and see me Monday. I'll have a new puzzle ready for you.