The LTC4412, or similar, probably won't be necessary,
depending upon Battery selection, and the design of the Charger.
I can't make a Battery suggestion because I don't have a
clue what you're building, or how it will be used.
.
.
.

Your preference adds up to ~6.3-Amps total Current.
Now You need to decide if You want to make sure that You have enough Power to
run run all those USB-Ports at their Maximum-Output, all at the same time,
or,
realistically, You will probably never use half of them at the same time,
and that will probably be somewhat less than full Load on each of them.
The latter will allow You to "get-away-with" using a smaller, ( Lower-Current ), Power-Supply,
or,
it will allow more minutes of run-time when You are on "Batteries-only-Power".
I'm not an expert on this, but I think the Specifications for Current-Delivery for
the USB-Ports is a good-bit higher than 0.5A and 0.9A .
Where did these Current numbers come from ?
.
.
.
No, I have no need to swap batteries in and out. My one and only concern is that supply power _never_ drops below some minimum value as long as batteries have some minimum charge.This is, of course, only one possible option ..................
Your "System" is powered by a built-in-Battery.
The cabinet for your System has a Jack on the outside for an external Power-Supply.
When the Power-Supply is "plugged-in",
it charges the Battery and provides enough additional Current to run the System,
both at the same time.
This is so very simple, that I'm thinking that there is some other problem
that You are concerned with that I am not aware of.
Why does this not make sense to You ?
Are You worried about having the ability to swap-out Batteries while the system is running ?
( this is not a problem, but it needs to be "specified" in the design,
because certain other factors must then be taken into consideration )
.
.
.
There are many highly specialized Chips that "may" or "may-not" be suitable for a particular application.
But, You have to understand exactly what factors need to be taken into consideration FIRST.
I keep begging You for a comprehensive outline,
a list of expectations,
a list of hard-requirements,
and a list of "it-would-be-great-ifs",
but I still don't have a clue as to what You're trying to accomplish with this project.
Everything is a compromise to some degree or another.
To make those compromises the most advantageous that they can be, a PLAN must be created.
A PLAN will allow You to weigh the relative values of all
the various options available, against each other.
The PLAN may change many, many times, this is to be expected.
Following a PLAN will result in the most satisfactory final-product that You are capable of,
which is, of course,
based on your current experience-level and resourcefulness.
A few places to start might be ..........
How many minutes must the Battery be capable of supplying ~25-Watts of Power ?,
2-minutes ?, 10-minutes ?, 30-minutes ?, 2-hours ?, 20-hours ?
What is the maximum physical-size/weight of the Battery that is acceptable ?,
( just remember that Power X Run-Time = more weight, size, and $$$ )
Does weight matter ?
( Li-Pos are half the weight of an SLA-Gel-Cell, but 2 to 3 times the cost )
Can the Charger/Battery be contained in its own remotely located Box ?
( if You need a big Battery, putting it on the floor under your desk makes a lot of sense )
.
.
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Ok, Thank-You,
That puts the Current over 7-Amps, for 2-hours,
that's ~14+Amp/Hours required of the Battery.
.
I don't think You realize what You are asking for, but here is a start ..................
.
This Battery may not fit into your existing Box, but it's very close .................
In any case, your Box MUST BE Aluminum for Heat-Sinking, no plastic,
Bud-Industries makes some nice Cast-Aluminum-Boxes .........
https://www.digikey.com/en/products/detail/bud-industries/IPS-3933/2499348?s=N4IgTCBcDaIEIFcAmACAkgBQMoFoDMAnHniALoC+QA
.
Battery ........
Chinese Batteries, in general, have very poor Quality-Control, and extremely dubious Specifications,
I will always recommend against them, even though there are a few reputable Chinese companies.
.
MaxAmps "description-Part-Number",
( they don't use part-numbers, almost all of their Batteries are custom-made ) ......................
https://www.maxamps.com/lipo-17000-2s-7-4v-battery-pack
.
"" LiPo 17,000 2S 7.4v Battery Pack, No Plug, 12-AWG ""
~$214.oo
Completely guaranteed Performance, and Life-Expectancy.
.
Size = 6.25" X 3" X 0.9", ( 158mm X 79mm X 23mm ),
.
Weight = ~1.5 pounds, ( 660 grams ),
.
( ask MaxAmps about optional "built-in" BMS Circuit-Board ), ( Battery-Management-System ),
( It may be more cost-effective than a DIY-Battery Protection-System ),
If You want a pre-warning Low-Battery-Alarm, and Switch-Output-Signal,
a DIY Low-Voltage-Cut-Out Battery-Protection-Circuit will be required.
.
MaxAmps, Heavy-Duty, 20-Amp-Peak / 5.1-Volt, Buck-Regulator ~$43.oo,
.
Battery-Charger ..............
>>>>Battery must be Charged, and held at, EXACTLY 3.8V + 3.8V = 7.6-Volts, ( +/- 0.1-Volt ) . <<<<
This Charging-Voltage will reduce overall Battery-Capacity by around ~10%,
but it will probably quadruple Battery Life-Expectancy, ( 2 to 3-Years or more ).
.
Battery-Charger external AC-Power-Supply .....................
DigiKey,
AC/DC Switching-Power-Supply, 12-Volts, 7.5-Amps, 90-watts,
https://www.digikey.com/en/products...a4BxzAWgIwFYAiBNAygTgAZkUwCB2NAgcSQDkMQBdAXyA
~$45.oo
.
Bullet-Proof DIY Switch-Mode-Voltage-Regulator, ~$60 to ~$100.oo, in parts cost.
Very questionable 10,000-Watts !!!, Chinese Switch-Mode-Voltage-Regulator on Ebay, ~$20.oo,
( remember how much money You saved when it goes up in a puff of Blue-Smoke, for no apparent reason ).
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