RunForTheHills' suggestion is the simplest and safest, albeit the slowest (as it will just charge at the rate you can already charge them at).
You need an inverter that can handle the total AC-side current of *all* the chargers you will have connected at the same time, *and* you also probably want a pure sinewave inverter, since the chargers may not be well-designed and/or unable to handle the usually-non-sine (dirty) AC output of many inverters. (I've blown up a few things over the years running them on common inverters).
Using another battery to store charge slowly from the alternator and then be able to more quickly charge your bike batteries has been done. But to do it you have to have a DC-DC converter that has the same kind of CC/CV output that your chargers do, or LED PSUs. If it doesn't, it won't regulate the current the way charging should be, and various problems with either the converter or the battery can happen, including destructive or even catastrophic failures.
Or the converter then has to feed a charger that does have the CC/CV output, but this wastes much more power and charging time--might as well just use the 12vdc-120vac inverter and plug your charger in.
fast charging (C/2) seems to be something Li batteries handle well.
That depends on the specific battery. The cells might handle it (many are made for 0.5C charge rates, some even higher), but the battery as a whole may not, either because of wiring, connectors, or BMS limitations.
If the wiring or connector isn't able to handle the higher current it will heat up; this may be insignificant, or if they were only designed to just barely handle the original current they may heat enough to begin to fail--insulation may melt, etc., leaving it vulnerable to a short depending on routing of wiring, etc. It's unlikely to heat the insulation enough to actually catch fire on it's own, though a connector that fails by overheating, if it's made of typical soft plastic, may allow gravity or charging cable tension to deform the connector enough to move contacts within the plastic and depending on connector design to short to each other or other parts in the battery, which could lead to a fire then, or later.
The BMS charge FET(s) can only handle a certain amount of current without creating excess heat; the board is usually packed inside the battery in a way that doesn't allow it to shed that heat very well (and any heat it does shed is going mostly into the cells nearby, rather than thru the insulating plastic case / etc of the battery pack). It's unlikley to be much of an issue, but if they used the cheapest FET they could that would barely do the original job, it might not do a higher current very well for very long.
Another issue is age. As cells age, various problems increase. For instance, the cells become (more) different from each other, and charge at different rates--the higher the charge current the more obvious this problem may be. The cells in general become higher resistance, and heat up more for the same charge current, so a higher than usual current heats them even more.
How much the above stuff ends up being a problem also depends on how long the higher currents flow, so the bigger the battery pack and/or the farther it's discharged the longer they'll flow while it fills up, and the more the heating in those things will affect them.
So, it's generally safer to use only the same charging current that the original charger for the battery supports.
If the battery actually has a label spec for a higher charging current, then that should be safe, too (depending on the battery source; cheap batteries may already be pushing their limits at the lower current).
