Is there anything out there that might be much less functional, but still allow me to split out and export the individual components as .obj files?
There is a way but it's a bit of work. On the other hand you'll learn how obj and mtl files work 
It mostly depends on how the object is structured internally but you would have the same issue in Blender too.
First make sure you have exported your kitchen from Sweet Home 3D. This is because Sweet Home 3D structures the obj and mtl files differently than for example Blender does.
If you open the obj file with a plain text editor (NOT MSword or other advanced word processor!) you will see lines starting with "g " followed by a line starting with "usemtl ". A "g " line is a part of the total object and the "usemtl " line after that references the material to use for that "g " part. Scrolling through the obj file you will see that multiple "g " lines have the same "usemtl " reference.
In Sweet Home 3D you can make materials invisible when you "Modify furniture". When exporting invisible parts will not be exported so that's a way to isolate a part from the complete object.
Of course that doesn't work if too many "g " parts use the same material. It would noy only make parts invisible that you want to get rid of but also parts that you want to keep simply because the yuse the same material. So the trick is to get different materials for each "g " line. You can do that by changing the "usemtl " line by replacing the material name with a new unique name. Of course you need to add that material(-name) to the mtl file. Just copy a block in the mtl file and change the name to the name you added in the obj file. It doesn't matter what the actual material is, you can change those later, it's just to seperate into unique material names.
First try it with just a few "g " and "usemtl " lines and after import see what it does. In Sweet Home 3D you will see the new names you added and the actual part ("g ") will blink in the preview.
Sometimes it's a very small part or even hidden by other parts so you might not see some of the blinking parts.
Long story short, and here comes the big work: Give every "g " it's own unique material name and add them all to the mtl file. If you now import the obj file you will see a long list of materials in Sweet Home 3D BUT it gives you the option to make every individual part invisible and that allows to isolate only the parts you want. With only those parts visible you can export/import to get the separated kitchen applicance. Rinse and repeat for every part you want to separate as an individual object.
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