Two notes:
The plates were not firmly pushed together. This does change the expected capacitance somewhat.
These results show repeatability and that high degrees of accuracy are possible.

Fully covering.
serial port options set
read 150
read 225
read 263
read 281
read 291
read 296
read 299
read 300
read 300
read 300
read 300
read 300
read 300
read 300
read 300
read 300
read 300
read 300
read 300
read 300

Approximate 5mm shift
serial port options set
 145
 219
 255
 273
 282
 287
 289
 290
 291
 291
 291
 291
 290
 290
 290
 290
 290
 290
 290
 291

Approximate 10mm shift
 132
 198
 230
 247
 256
 259
 262
 262
 263
 263
 263
 264
 264
 264
 264
 264
 264
 264
 263
 263

Approximate half plate overlap
serial port options set
 124
 188
 219
 234
 241
 245
 247
 248
 248
 248
 248
 248
 248
 248
 248
 248
 248
 248
 248
 248

Approximate quarter plat overlap
serial port options set
 121
 182
 212
 227
 235
 239
 241
 242
 242
 243
 242
 242
 243
 243
 243
 243
 243
 243
 242
 242

No plate overlap
serial port options set
 104
 155
 181
 194
 200
 203
 205
 206
 206
 206
 206
 206
 206
 206
 206
 206
 206
 206
 206
 206