Andymark provides a .STEP file on the Sonic Shifter page, but when I open it in Solidworks, the entire assembly is undefined, lacks materials, is completely unmated and has some of the wrong parts for my application (drive axle and shifter). What is the best strategy for turning this into a usable model?
That’s what a STEP file typically is. It’s supposed to be compatible with any CAD package you want, so it won’t have feature trees like parts you model yourself. You can’t have material types or mates in a step file.
Before we can answer your question about turning it into a usable model, we need to know what you plan to use it for.
I would suggest going through and defining everything you need and then removing the parts you don’t need.
I did eventually bite the bullet and define everything. For those interested, I’m drawing up a WCD chassis concept that we will likely use for this coming season. I think everything’s good now.
I typically just select and “Fix” everything in the assembly when I first open it (select part in design tree -> right click -> “fix” ).
If there are specific components that need to be re-positioned then I go back and “Float” them before mating them to other fixed components. I haven’t had any problems yet.
This is what I usually do as well, for example with the Vex ballshifters. Then I update the weight of the assembly as a unit.
If the assembly is modified, I just keep the same weight unless there are some really dramatic changes, in which case I add materials.
This is the quick easy “fix” but is also an incorrect way to solve the problem. Fully constraining your parts is crucial in a complex assembly. It is a good practice to be practicing the right way to do things. Before teaching I worked in the CAD department for Parker Hannifin, and when modeling complex manifolds there was always a lot of part overlap with other assemblies. It was very common for another designer to take a complete assembly and remove individual components and replace them with customer requests. When constraints are done properly (using datum axis and planes when possible) this is a quick task. When done through the method you describe it makes other people’s days more difficult.
To the OP, re-constrain the whole thing, if nothing else it is 15 minutes of good practice.
I came to the same conclusion, so I decided to go through with everything. Now if only all of the gears were actually modeled and messed 
I would agree for any assemblies you are likely to customize or modify.
The vexpro 3 CIM Ball Shifter comes in as over 60 individual parts and contains 3 subassemblies down to the balls in the shifter. Regardless of the gearing spread used, the mounting points and overall size of the gearbox does not change except for two external gears. I would be impressed to see it fully constrained by a student in 15 minutes. Half the time I delete all the internal gears to make it load faster in the assembly.
The sonic shifter has fewer parts and could probably be constrained in 15 minutes. It is good practice, especially if you haven’t physically assembled one before.
Unfortunately in FRC I’m often using the CAD as an easy mounting pattern reference.