Finally got the panels somewhat round. Also got rid of the FPGA dev board and designed my own. The power supply solution has been revised.
While the electrical interface specification of HDMI is close enough to LVDS so that the IOBUFs of the FPGA can directly interface to it, there is no propper on-chip termination for HDMI available. So the termination network has to be implemented off-chip and the dev board really messed up the signal itegrety. The traces where way too long and also more designed to turn lights on and off, as opposed to differential, controlled impedance pairs. A nice side effect: My own board is much smaller, lighter and also has the correct connectors on it.
On the power supply: The panels use up to 14 A. I planned to use a 1S Li-Ion cell and boost the voltage up, but, as it turns out, the 20 A habor freight boost modules can’t even supply 3 A at single cell voltages. Bummer. So the plan got changed to stepping down a 2S cell stack. At the prices of ready made step down modules there is no point in designing my own boost regulater only to be able to run 1S.