No pain, no gain...
My big thanks to the volunteers who accepted the challenge.
It's perfectly possible to upgrade these equipments.
The SHS800 series (804, 806, 810 and 815) behave as a SDS1000CML. If you run a SCPI command "MD5_PR?" they will report the product_type "SDS1000CML".
So, I guess looking at the FW, the SHS820 series (820, others?) behave as a SDS1000CNL. Anyone with a SHS820 can confirm this doing the "MD5_PR?".
(And that validates the HWs are really different beteween the 2 series and their corresponding FWs.)
But if that is the case, and since the FW has references to the SHS830 model, maybe it's perfectly possible to upgrade a SHS820 to a SHS830 (300 MHz).
The results so far, are attached.