Using solar power on a dual inverter setup simultaneously, that share different parts of a series battery bank
I had an idea and wanted to present it here and ask if anyone foresees any problems with doing this... I have both a 48VDC input inverter and a 24VDC input inverter that I want to run from a 72V series bank of batteries (six identical 12V batteries in series). So imagine the batteries lettered sequentially A thru F, the 48V inverter would attach to A+ and D-, the 24V inverter would attach to E+ and F-, and the solar charge controller would attach to A+ and F-.


Batteries to be used in series banks should always be matched and balanced before connection and discharging them in this manner will unbalance them unless you use some advanced battery balancing circuit.  Testing an already used battery for match and balance is an advanced task.  You would also have to design and build the circuit yourself as in almost every case this situation is to be avoided rather than worked around.  Exceptions are things like taking a nanoamp voltage reference from some subset of cells.  No currents of consequence though.


  So the idea is to use a high voltage battery bank since the solar charge controller (scc) I am using is a boost converter that requires the battery bank voltage to be higher than the solar panel input voltage. To get the maximum power out of the scc, I have to feed it close to 60V input, which means my battery bank has to be 72V or higher.  


Nothing wrong with using that voltage, but you would need to get an inverter with the correct input voltage or switch to a voltage that is compatible with one of your inverters.  


  I will attempt to load the 48V and 24V inverters about equal (in proportion to each other), 


Your two inverters will have different loads and efficiency curves so even if you matched the loads you connected flawlessly the loads on the batteries would be different anyway.  To produce adequate accuracy, you would need a specifically engineered solution, significant difficulty for someone with an EE degree.


  so that the 6 individual batteries are in a similar state of charge (SoC), and so that the scc should charge them all about equally.


Because of permanent effects of charge and discharge on the batteries, it wouldn't be adequate to maintain a similar state of charge.  You must maintain a similar state of charge, but also a near identical charge/discharge history.


  So will/should this work? Anything to "watch out for"?


Funny you should phrase it that way.  This connection method in itself is fraught with peril and is in itself something to "watch out for" ;D.  

Just a further note, batteries are a significant part of your system cost.  If you wanted a 6s(72V) battery bank, if you want to replace a battery and you don't know how to properly match, maintain and test them, you're stuck with buying batteries in sets of 6.  In many cases battery cost is greater than converter cost for a system.  I'm telling you not to connect this way so you don't end up with a house fire, but even if you just damaged your batteries or wore them out faster you might spend more money than the correct equipment.

Edits/Additions:
Regarding your proposition regarding load balancing, note that if your small inverter provides 500W to a load, this will require a different amount of total battery power per battery than if your large inverter provides 1000W.  Wear on the batteries will be based more or less on the total currents, both charge and discharge, with larger currents wearing out the battery faster.  If you draw 10A for 1/2 hour, that will wear the battery out more than if you draw 5A for 1 hour.  Given this, it is more or less impossible to balance battery wear properly and difficult and labor intensive to actively match batteries.  The labor cost exceeds the cost of new equipment by an order of magnitude, even at minimum wage in most areas.  Your time has value.  Also if your system just happens to charge when your batteries are a bit imbalanced, it will cause battery wear on those that are overcharged.  If it happens when they are more imbalanced, rapid failure of 2-4 batteries, possible outgassing/fire, so you had better be sure to check and charge them frequently enough.

Regarding connection of equipment in unintended manner:  The casing and ground contacts of your inverters have to be grounded on at least one of the input or the output.  It likely has multiple internal connections to ground through it's electronics in addition to the bonding wire.  Unless it is intended specifically to be used on an isolated-from-ground battery.  In most cases the negative DC terminal will be grounded, so when you connect both inverters and their grounds, you will be creating a 48V direct short.

Series arrangement of batteries - This is very important for large batteries/banks.  The batteries should be matched in characteristics, before being combined, not just matched in voltage, but ideally brand new identical batteries, obviously from the same manufacturer.  They should be grouped up and never charged or discharged separately.  Maintaining a bank where load is uneven or batteries are rotated requires a professional level of skill, aside from the large effort.

As of early 2019, $120 for the crappiest versions of a 3kw 72V inverter or $20 and $65 for a 500W and a 2000W if you actually want two inverters for efficiency reasons.  I'd consider shopping around for a 2-3kW inverter with good efficiency and a flattish efficiency curve.  

I won't tell you not to learn the way you want, but do so knowing this is a very bad idea and do everything possible to mitigate the dangers.

Be sure your battery storage is up to code or exceeds it if necessary. Depending on where you live there may be no code or you may be required to have a metal box or a specific method of venting.  Nothing crazy.  If you were to have a house fire that started at your battery bank and this setup was found to be the cause, it will in all likelihood void your homeowner's insurance unless the insurance company neglected to check.