In my personal experience with HF Pactor e-mail, Iridium, and Globalstar the system you already have may be most effective. Note that the overwhelming majority of my experience is well offshore and may not apply if you are island hopping or lingering in anchorages.
I have found HF e-mail to be extremely robust and reliable if a bit slow. If you are having difficulty easily making connections perhaps a "tune-up" on your installation and some attention to the ICEPAC add-in to Airmail is appropriate. Iridium is more reliable than Globalstar (and accordingly more expensive) but even so does not meet the standard of Pactor. The actual connection may be faster but the time one spends getting a connection that holds long enough may end up being a greater burden than HF.
My Inmarsat experience is quite dated so probably not relevant.
If you are island hopping in the Bahamas and Caribbean you may find an investment in good wifi gear to be more cost effective than satellite equipment.
sail fast and eat well, dave
beware "cut and paste" sailors.
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