Hard to say without seeing your data and working through some exploratory analysis. Some more details on hypothesis, sample design, and actual data collected, would be welcomed. When asking statistical methodology questions it is important that you state the hypothesis that you are testing. This can dictate statistical methodology and without knowing, we are shooting in the dark.
It is also not at all clear what the issue with the specified statistics is in relation to "not giving me what I want". I do not know what you expected with a univariate autocorrelation statistic indicating a bivariate spatial correlation. The family of SCAN statistics is quite variable with many defined distributions available. What distribution (model) did you define in SaTScan and do you actually have a hypothesis, and data, suitable for a point pattern analysis? Generally, a gridded, systematic, sample is not appropriate for a point pattern analysis.
A correlation would be very limiting from an inferential standpoint and it would seem that a regression type mode is in order here. At first blush I would think a mixed effects model with an AR-I term for time and a autocorrelation term for the spatial random effects would suit your needs. This would allow you to partition variation by time and normalize any influence autocorrelation would have on residual error and iid assumptions. Another option, if the data supported it, would be a Poisson point process model in an MCMC framework. If specified as a hierarchical model you could define time as a prior. With a kernel regression approach you could test multiple hypothesis of spatial diffusion processes or define a quadratic diffusion term. This type of model is commonly used in spatial epidemiology to get at rate of spread.
It is easy to get lost in "throwing your data against the wall" with spatial statistical approaches but, unless your sample design was intended to capture spatial process and you have a well formulated question regarding spatial effect, this can be a futile exercise.
Because of the easy availability of methodologies frequentists methods are often overlooked. There are regression models available that can readily deal with spatial data (spatial and conditional autoregressive, spatial regression, polynomial regression, mixed effect models, canonical regression, kernel regression, semi and non parametric regressions, ...) and if you are intending on inference these should be explored in relation to your hypothesis.