Few chargers run on both AC and DC and fewer still come with multiple units inside. Even then, I'm not sure how many are multi-chemistry. Worse yet, none can quickly charge what I consider to be a large pack.
To handle both AC and DC most of us buy a separate power supply. I won't go into the advantages and disadvantages, but if you can concede this point you will find many very high powered and economical chargers. Also, internal power supplies are often limited to 50-100W which is not high power. And if you really do want high power you'll need to step it up to a 24V input.
Since your charger doesn't exist (that I am aware of) I am going to suggest the following setup:
1) AC power supply with 24VDC output, capable of at least 500W output (you could start with a 12-15V supply and upgrade later if needed)
2) Multi-chemistry charger of at least 20A and 300W output with a 24V input capability
3) Learn how to charge batteries in parallel
My pick for the charger would be an FMA PowerLab8, or iCharger 208B, 306B, or 3010B. Hands down the best charger is the FMA PowerLab8, but it may exceed your budget.