The old machines worked very well. My magimix was about 10 years old but since the smaller ones that have the programmable water amounts came in they don’t work on non pure sine wave
FWIW, the Krups machines I found all seem to be 1260W, which will require about 110A from your batteries allowing a little for conversion losses, which seems a sizeable hit even for 200Ah of Li. YMMV, but that seemed a little excessive for me, which is why I suggested some manual alternatives that will deliver a good espresso without stressing your electrics. That said, your OP said that your Krups machine wouldn't work with the sine-wave output of your inverter. Since mains electricity is sine-wave, I suspect you either don't have a pure sine-wave inverter or its capacity isn't enough.Lovely people whilst I am enthralled by the virtues of the aeropress, I just want sump oil espresso and I need to know which machine will run on my inverter. Someone must use one...
I would imagine your coffee machine will require around 1500 watts to work, as will any other machine, and as your inverter output is 2700w, it should work ok in theory. I can only think your inverter is faulty or it’s output is less than it states.the output is 2700 watt. So more than capable of running a small coffee machine.
FWIW, I suspect the Krups machine has a low voltage cut-out and maybe your kettle and iron don't. That said, if those 17mm dia cables are connected directly to your battery +ve and -ve and the cables connecting the batteries together are of similar size (or at least a conductor of 120sq mm / 12.5mm dia) then you are probably correct. However, inadequate sized cable anywhere in the 12v circuit to/from the inverter will probably hamstring it.
I had a similar problem, after installing an inverter 2kW to mainly work my tassimo machine but it wouldn’t work, I then decided to upgrade my machine to a nespresso en550 highly recommended by Geeky Phil but this too didn’t work however other things did work with higher wattages ! A bit of googling on the internet found many people with same issue. The problem was my inverter was a “modified sine wave” so I bit the bullet and bought the equivalent 2kW “Pure sine wave” inverter and everything worked fine ie, both the Tassimo and nespresso coffee machines. Maybe your inverter isn’t a Pure sine wave?