Is the Delay in Strain Data Due to Capacitance?
A board capacitance * metallized strain resistance time constant is likely to be in the millisecond range.    However the self-heating from I^2R thermal effects and temperature coefficient of the material is more-likely to have a time constant of a minute, if I imagine your design correctly.   

Try lowering the bias and/or drive voltage to prevent self heating and increase the filtering of the noise to improve the signal to noise ratio at higher gain needed to achieve the same sensitivity.