I'm working on designing a table for my kitchen (no A/C for moisture control) and I'm not entirely sure what the best method for securing it would be, and if I should even bother accounting for expansion/contraction at the size of this table and the material.
I think the simple answer to this among professional builders would be, the same method I always use. Within reasonable limits smaller or larger doesn't change how they approach attaching a solid-wood tabletop to an apron or other understructure, they do what they always do because it's the safest approach.
And 20" is wide enough that you do have to give a thought to movement, unless the local conditions are unusually stable which you indicate they won't be. Even if you were using quarter-sawn material1 it might be wise not to screw directly to the leg assembly.
The reason I'm hesitant to go to something that would allow for expansion and contraction is my worry that it would allow the tabletop to move if bumped or when the table was moved
Well think about whether this seems to be a problem with all the tables where the top is attached that way. It's not, so it won't be on your table either.
With the most traditional tabletop fastening method, hardwood buttons, there's sufficient friction between the buttons (typically only four on a small table but could be as few as two) that the tabletop simply can't be moved by hand, or by a bump from a hip. If it could be the screws fastening the buttons aren't tightened!
And it's the same story with any of the modern metal substitutes for buttons.
along with the added complexity and some limitations with tool availability
To be fair buttons aren't something everyone is set up to do easily. However, virtually any woodworker can make and install them with even the most basic hand tools2, it just takes a bit longer. Make the buttons in a production line, drill/countersink the holes, do all the grooves or pockets one after another and you'd be done before you know it.
With arguably the best of the metal substitutes for buttons tool availability pretty much stops being any issue as they are surface mounted, they simply screw in place3.
1 Which has a much lower coefficient of expansion, roughly half for many species.
2 Saw, drill, chisels, hammer, marking tools.
3 So at most you need a drill with a small bit (or a bradawl) for pilot holes and one screwdriver.