Hi, Craig,
Regarding your question, I recommend you use Kinetis KM family or KL family.
Because you test the strain gauges signal which is differential signals, and you do not want to use AMP to convert the differential signals to single-end signal, so the required ADC must support differential input.
At the time being, the Kinetis has two ADC module SAR ADC and AFE(Analog Front End), the SAR ADC supports 4 channels differential signal inputs(ADC0_DP0/ADC0_DM0, ADC0_DP1/ADC0_DM1, ADC0_DP2/ADC0_DM2,ADC0_DP3/ ADC0_DM3), but the SAR ADC does not support programmable gain feature.
The AFE module support differential analog input with programmable gain, the maximum gain is *32.
The KL family is a low cost and low power processor with SAR ADC and the required serial port(SPI,IIC,Uart), but the sar ADC does not support programmable gain, for example you can refer to KL43.
The KM family has AFE module, but it needs more power than Kl family.
This is KM family link:
ARM Cortex-M0+|Kinetis KM3x 50-75 MHz 32-bit MCUs|NXP
This is KL family link:
Kinetis L Series Microcontrollers - Arm® Cortex™-M0+ Core|NXP
Hope it can help you
BR
Xiangjun Rong