I would like to clear up a few things.. Iridium and Inmarsat actually work on different frequencies. Inmarsat actually works on a range of frequencies and the system chooses the frequency based on several factors. When the Inmarsat system chooses the lower frequencies it causes interference with the Iridium system. Typically the BBJ will have a high gain Inmarsat Antenna which directs the SatCom signal directly at the satellite – when the signal is crossing over the Iridium antenna due to the location of the satellite it is connected to and the heading of the aircraft the interference will be present. There are a few filters available – one goes on the Iridium RF cables and blocks Inmarsat from getting to the Iridium Transceiver, this filter type has shown to not work well. The other filter type goes in the Inmarsat System and blocks the lower Inmarsat Frequencies, this filter works well but I do not believe it is approved by Inmarsat.
Your Inmarsat HSD440 system uses SwiftBroadband for cabin internet and uses AERO H, H+ for ACARS – this is a separate channel from SwiftBroadband. If you are running ACARS away from VHF coverage and it works it means your connection through the Inmarsat Aero H, H+ is good. CPDLC is a part of FANS 1/A which includes both CPDLC and ADS-C and travels inside the ACARS message set; once it reaches the ground CPDLC and ADS-C messages are routed via another path to ATC. That path to ATC could be broke. But since you say the entire system becomes inoperative I would suspect something in the aircraft – sounds like software lockup. Your service provider should also be able to check the CPDLC login and see if it is reaching the ground and if there is a break in that network somewhere.