Well done Barbara! Bandsaw boxes can be fun and easy projects but they also definitely present challenges! You discovered one, which is make sure your bandsaw is in tip-top shape for best results. And all bandsaw boxes have "sloppy" drawers, it's just the nature of the beast. One thing I've found that snugs them up is to widen the kerf going into the drawer and then glue the kerf closed after cutting out the drawer. This does mean though that (a) depending on the geometry, you may have to sand the drawers down in some spots to make them fit and (b) you will loose grain continuity when you reattach the back and will probably have to flush trim/sand it because it will have a little overhang.
Another way to close up the gaps in the drawers is to use a different material for the drawer fronts. When you cut the front off the drawer, use it to cut new fronts from a different material (or the same material if the grain continuity isn't an issue) that's slightly larger than the drawer and fits snug in the hole. When you do this, the drawer may sit crooked but you can either do the same thing for the drawer back or put some slick tape to level it up. Below is a box I did where I used this method. I really like the creativity that bandsaw boxes allow. But the gappy drawers really irritate the woodworker in me!
You can't tell it in the photos, but I used a "wine colored" flocking in the drawers. Instead of slick tape on the drawer bottoms, I flocked the inside of the drawer compartments as well.
Another thing I try to do when possible if doing drawers fronts by this method is to incorporate the kerfs into the design and not glue them shut.
