You seem to misunderstand what a modified console is; just because it has Custom Firmware installed does not make it a "pirated switch". Nintendo Switch consoles that are exploited to run custom code can connect online without getting banned; people get banned because they pirate and install games rather than purchasing the cartridges/buying it on the eShop.
If your console is banned, then you cannot connect at all to HOME.
You need a legit console, a legit copy of the game, and custom firmware running on the legit console in order to modify your save data.