, great! Full-disclosure: while I am a woodworker who makes furniture, I am a plastic model builder and haven't yet attempted to do what you are now. That being said, I am very familiar with the tools you are using. The first thing I would make certain of is that my bandsaw table is perfectly square to my blade and that the blade is properly tensioned and tracked so that there is no deflection in the cuts.
I think where you may be running into trouble is with this kind of belt sander which, while there is a support behind the belt to work your shapes against, the edges of the belt don't lend themselves to getting neatly into tight corners. It is very easy, using this kind of belt sander, to introduce irregularities to your surfaces, which may be what is causing your gapping difficulties.
If I were attempting this, I would bandsaw close to the lines, as you have done. I would then make up a series of sanding blocks and sticks. The main sanding block should be large enough to manipulate comfortably, and the sides need to be perfectly square to the faces. To the squared edges, I would double-stick tape 100 grit sand-paper. This block, set flat on a flat work surface, is what I would use to fair my convex curves. I would make a corresponding, curved face block that I would use to fair my concave curves. The advantage of these blocks is that you always will maintain squared edges on your parts and the solid backing of the block enables you to shape reliably to your lines.
Likewise, files can be tricky to use. For this sort of thing, I prefer to make sanding sticks to which I double stick my sandpaper. These sanding sticks are for the final tuning of the joint. Patience and a lot of back and forth checking will ensure that you ease into adjacent steps and shoulders without introducing slop, elsewhere in the joint.
This isn't exactly an easy thing to do, but it is certainly an acquirable skill, with patience and practice. The benefit of mastering this skill is that it makes the scratch fabrication and fitting together of the many parts and deck furniture an enjoyable pass-time.