I used a fishing tackle box for model building while on Army deployments. Mine was a Plano brand box with 3 fold out trays on each side, plus a large open compartment on the bottom. The trays hold lots of supplies, and the bottom can hold a 1/35 armor kit, but it will likely need to be repackaged. That compartment is not made to hold a model box. It has also held 1/24 cars and 1/48WWII aircraft. I have searched for a larger tackle of the same style, but apparently there are none in production now. There is another type which holds organizer boxes. Plano makes a couple of big ones. I have their 787 and 1374. One holds 4 organizers and one comes with 7; 4 big organizers and 3 smaller. They also make other organizers with the same exterior dimensions but different internal layouts. If you want, I can post pictures comparing the three different boxes later on. I also have additional organizers with different internal layouts. The type with built in trays that fold out is several years old and may be out of production, but they do have a similar size box of the same style in production now.
I would agree that an ammo can or anything that could be thought of as suspicious...by any misinformed citizen...is a bad idea. Nobody needs a SWAT team busting their door down at 3am.