In case anyone else comes across this problem (and is unfamiliar with more advanced ODE principals, as I am), I believe what I attempted to describe in my post here is an example of forced system, for which there are excellent resources and links discussed here.
I’ve since reformulated my model such that this forced approach is not necessary, and instead, we model the effects of time by capturing the change in a parameter when a single ODE system is simultaneously fit to all the data, and where binary indicator variables enable different versions of the parameter to initialize for the different time periods of data. In short, @Funko_Unko, I am indeed following your suggestion of running in parallel :-)
Thanks, folks – the resources accessible on this forum are really helpful!!