Generally speaking both the template and analytic fitting seem to underestimate the baseline and peak amplitude of the pulse. A couple of things to investigate, some requiring new code, some not:
weighting the fits. perhaps configurable as an option
alternative functional forms for analytic fitting
fit less baseline (simply reduce range in the config file)
fix baseline somehow (possibly also configurable as an option)
Generally speaking both the template and analytic fitting seem to underestimate the baseline and peak amplitude of the pulse. A couple of things to investigate, some requiring new code, some not: