New

There is no need to worry about the C rating in your case, your 0.6C battery bank can give you 6000w which is more than what you inverter can invert as long as you have the correct gauge wire and fuses installed. 
While a lower current is more suited to release the remaining energy inside the battery, LFP batteries do not suffer noticeble reduction in capacity when being discharged at 1C. Put differently, with decent LFP battery you will get close to rated capacity when discharging at 1C, you will not notice the difference.
Charging at high C ratings should be generally be avoided. When charging occurs at very high currents, the heat generated within the battery cannot be removed fast enough and the temperature quickly rises.

PS the BESS app shows all 16 of my cells in each pack to be at 3.32V most of the time
As of right now the master battery is 16 cells @3.32v my slave battery has 13 cells @ 3.32v and 3 @ 3.33v - even when I've had the weird drops and such the cells are all according to the app fine and within normal range - and I've never had  the actual pack go into a full on fault mode other than once for a low voltage level 3 fault when they where completely drained and we had no power for 12+hrs
Anyway I hope you fair better

Welcome @New
As you can see I've not had a great experience - your SOC cycling between 90-100 suggests 2 firmware version earlier than mine now after 2 updates - mine did that originally - purchased in Nov 2022 you can see in the post how to determine which batch and version battery you have but if you bought it in the last 3-6 months its the v3 most likely - mine is too.
My advice - don't update the firmware if you're not having any issues - I hope unlike me time doesn't paint a different picture - if you can get below a 20% SOC then you're already better off than I am, whenever my batteries hit 40% SOC they'd drop to 7/5/1% in 2-3 minutes.
Maybe as a caution, C rating doesn't stack as people think it does - I've seen multiple installers, resellers etc. say that 2 x 0.5C batteries gives you 1C. That is not correct. Assuming you have 1, 4 or 8 of the same battery rated at 0.5C your storage capacity is doubled, quadrupled etc. but in essence if you want to realise that stored energy as efficiently as possible then you would need to use it at 0.5C or even possibly 0.25C
Basic rule" C rate doesn't stack in Series
In parallel connection the C rating is wrongly attributed to stacking the load because you're "1/2 ing" the current between for example 2 batteries - think of it this way the faster you discharge them "Higher C rating" the less electricity you get out over time.
At it's simplest Its the electric car example - lets use a TESLA - freekin quick but if you thrash it in 01-100 launches and max performance pulls what happens - batteries overheat and your range i.e. usable storage disappears and becomes much less. fast = more power, more power = higher C rates 2C, 4C 8C etc.
I used to in a previous life fly large commercial load-bearing drones - we'd have large LIPO packs that you could pull/discharge at 25-40C for about 2-3min in specialty situations and then they'd unceremoniously die or you could fly reasonably at 8C and get 10-12min
If you where unlucky your drone would plummet out the sky or if you where a good pilot you'd monitor voltage and current like a naughty kid in a park and landed it just before it was about to expire - I was one of those pilots that was careful and I have only ever lost one drone - I "infamously" drowned a very large, very expensive drone 10yrs ago that had a faulty BMS and I ignored the V and C rates for 5-10 seconds - it landed itself in a large dam - police divers had to come fish it out. Needless to say my "employers" where not happy with me - however telemetry data proved I wasn't reckless and that the BMS went "offline" about 15seconds before the drone became "unstable" - the lesson applies though.
200AH batteries discharged at 2C will not nett you 200AH worth of energy.
CFEs own data is misleading - an older manual states 5000w/3000w nominal i.e. 0.6C, the sticker on the side says 100ah or 1C and newer docs mention neither other than 1C charge and discharge - they cannot seem to decide which one - I would have to advise based on my experience that you treat them as 0.5C for charging and discharging.
My beef with them is CFE sell there batteries as 1C charge and discharge product - It cannot in my case reliably do 1C between the 2x 5.12kWh batteries and in Lithium mode the batteries die in 17min or less - now whether the SOC is wrongly calculated, comms are faulty or my batteries are not charging fully or discharging, I don't know, but we cannot spend the type of money we do on these to tinker - If I wanted to do that I'd build my own battery packs.
My advice after 7+months - there is no need unless a once-in-a-blue-moon emergency to charge your batteries at 1C - 100AH, i'd recommend not acceding 0.5C or 50A and I found 40A is a nice middle ground leaving your inverter some headroom to run other loads when charging - again ideal on a 8kw invert but I'd drop that to 20-25A on a 5kw inverter.