If the total sample is 4mm across then OpenFlexure has 12mmx12mm range, so it should be fine. Though it will take some time to capture the whole sample.
@JohemianKnapsody and @dgrosen can tell you all about the scan and stitch functionality of the OpenFlexure. Getting it to automatically upload to the cloud should be possible.
OpenFlexure has autofocus, the autofocus algorithm may struggle with fluorescence images due to the dark background, this is because the current autofocus algorithm uses JPEG compression size as a metric for focus (as the compression is done on the GPU making it fast). A paper is available on the algorithm that we use.
Fluorescence has been done with OpenFlexure both for the OpenFlexure Microscope and for the OpenFlexure Delta Stage. The hardware for epi-fluoresence and for the delta stage haven’t gone though anywhere near as much testing as the microscope has, and the code could do with a lot more tidying, to make it easier to develop in the long term.
It may be possible to illuminate from beside the objective. The issue here will be getting uniform illumination. Also I think seeing as the light is coming it at an oblique angle over a very large area this will create more unwanted background. Also by illuminating the whole area you may photobleach areas before you have time to image them.
As for filters, I think whether you can use lighting gels or need more expensive filters will depend on the interaction you are looking at and how far separated the excitation and emission wavelengths are. I know that the Enderscope used lighting gels.
Overall, the OpenFlexure designs should get you one the way to doing what you want. But I think it will certainly be a research project rather than a standard build from the instructions.