ayreon

This makes little sense.  Why 3x routers?  And why do you power 2x DSTV decoders if you only power one TV.  The first rule in L/S is to reduce your power consumption by as much as you can, especially if using lead-acids. 

Your Telefunken TV is an old LCD.  LCD, by definition, uses cold cathode fluorescent tube backlight technology.  New TVs use LED backlighting.  LED TVs consume approx. 50% less power.  Considering how super cheap a new TV is (in comparison to batteries) it would be a wise choice to replace your primary TV.

You have a 120Ah battery.  Even if the battery is only discharged to 50% SOC, that would mean you would need to replenish 60Ah.  That intelligent charger seems to be a PSA008 - it can charge at a maximum of 8A.  So it would take 60Ah / 8A = 7.5 hours. recharge time.  In reality it is even worse because the battery has losses (converted into heat).  You need to put more than 10Ah in if you want to draw 10Ah.
 

Looking at your inverter  specs sheet shut down volts are battery killer volts.
On your setup,  no you can't replace your deep cycle  battery with lithium 
To go for lithium you will have to buy an charger that can charge lithium and they not cheap .
So my advices is save your self all the trouble of buying bits and pieces to make your system reliable and battery friendly and buy an hybrid inverter and if 12v setup is all you need then for around R10k you can buy an 12v hybrid inverter with 100ah lithium battery and you should be good then for years of more load shedding 

I think this is extremely important information. People generally think that "Deep Cycle" means you can do it all the time (I did in the beginning too), but it is really meant for emergency situations, like getting your boat to the harbor before dark or something like that.

Just a few points. 
Based on what we know the battery has taken a knock that's why you only get 1.5hrs run time. 
Further we all want the fastest charger which if over about 18A will further shorten their life due to daily LS. Try and reduce your load as you have control over what you switch on. 
That 120Ah battery when new had 1440Wh of power up to totally discharged. To get a good life of over 18 months you should not use more than 720Wh before recharging. Not easy due to short periods that you can recharge before the next LS event. 
The 11.8-12V discharge level I mentioned will have to be implemented to save what you can save. 
Your current inverter should only cut out at about 10.5V being too low. 
I still rate this R100 voltmeter a good starting device to guide you when to reduce or switch off loads during LS. 
The next item will be a Victron battery protector to cut the battery off when reaching the 12V level. R900 is cheaper than replacing the battery every 6-9 months. 
May be share a close up picture of the charger you are using. 
Although the Telefunken has a 95W power supply it might draw 40-50W during operation. Thus for 4 hours it will use about 200Wh of power plus 15% due to losses from the inverter. 
 

You charging batterys to float charge and so they not fully charged at that volts and so it  can take hours for them to reach full charge at 13.3v float only . 
You did not say what inverter you have but sounds like it is just an bench  inverter and not an sin wave hybrid inverter as you using an smart charger .
The problem with smart charger you can not set the bulk and float charge for the specific battery used and so you mite be undercharging or over charging your battery NOT good 
The problem with these normal cheaper bench inverter is you can not set the shut down volts so you over discharging your batterys NOT good  . 
In the end such an setup is going to cost a fortune on batterys or having to  constantly babying the system to prolong battery life .
If 12 v system is all you really need for the basics and load shedding solution then you get same nice hybrid  sinwave 1.8 kw inverter for around R4500 so allowing you to setup charge volts and shutdown volts for the type battery used . 
 

Totally agree. Everyone wants to get the maximum runtime, totally understandable, but that's the nature of lead acid. You just can't deeply discharge them more than a dozen times; "deep cycle" really just means that these are not starter batteries. But they still should not be discharged more than 50% depth of discharge, except a few times in their life. Lead acid is a really bad fit for regular load shedding, when used with default settings that assume very infrequent deep discharge, like once a year at the very most.

These batteries should not be discharged lower than 11.8V under load or 12V with no load. They were over cycled due to LS nearly daily. 
Not sure if the takealot unit Can run on lithium. Provide the complete name and model and if a sticker on the side place it here. 
10.5V disconnect gives good time on battery power but kills the battery in a few months as you found out. 
Further the batteries should be charged to about 14.1V. The 13.3V via clever charger was also too low and contributed to early death due to being under charged all the time. 
Check how much power the TV uses. The 3 routers and laptop charger without TV should give about 7 hrs run time.