Connecting different lipo in series to achive high voltage
You can connect cells with different capacities in series if you handle intelligently the fact that they have different capacities, by charging them separately perhaps, and by detecting the end point voltage on all cells individually. This would mean you always had to charge it like a lab experiment, rather than an easy-to-use battery.

If you connect cells of different capacity to a standard BMS that is expecting cells of the same nominal capacity, then you could confuse it. What it would actually do, faced with different capacity cells, depends on its software, what it's been programmed to do, how clever it's supposed to be.

In the best case, it would take excess time during charging keeping all the cells at the same voltage. It would have to charge the capacity difference at low current through the cell voltage monitor lines, rather than at high current through the battery terminals.

In the worst case, it would declare that there was a larger than threshhold diffference in capacity between the cells and so think the lower capacity cells were broken, and refuse to work.

Re-reading your question, I note that you also want to use different types of lithium, a mix of LiPo and LIon. The latter use slightly lower voltages. I doubt that you will find any BMS that can be set up to mix the two types. While calling them all LIon is conservative for charging, you would need to call them all LiPo to be conservative for end voltage. You can still charge, and monitor discharge manually, on a cell by cell basis.