Wildebus - did you try running your fridge from a 375VA Phoenix inverter, or are you just guessing it won't run it, or allowing a safety margin? The peak your fridge drew was around 5-600 watts. The peak for the 12/500 is 900, for the 12/375 is 700, so I wonder if it would do it. It's only that high for a very short time.
The fridge failed to start with the 375VA Inverter just as it failed with the 250VA Inverter.
I was able to get more accurate info on peak current draw as my equipment changed and I saw the peak was greater than 600W. I have more information on this blog post -
https://www.wildebus.com/blog/products/selecting-the-right-inverter-for-an-ac-fridge/
I'll post a key graph here to show the load that is possible

EnergySnapshot - V&C (noted) by
David, on Flickr
Note that the 12/800VA unit still overloads everytime the fridge starts, so if an 800VA Inverter overloads, then a 375VA with a similar peak ability similar to the normal running ability would be hard pushed to be suitable.
See the graph below for a 800VA Multiplus

MP800-FridgeACvsOverload by
David, on Flickr
Now bear in mind a characteristic of the way the data is sampled means that the peaks are not always captured (the data is sampled just once a minute; the peaks only last 1-2 seconds), but the overload situation is noted every time on an inverter that can run at upto 650W continuously.
Is the fact the inverter goes into Overload an issue? not if it is designed that way. From Victron ...
“Full bursts – High Peak output
Some electronic devices – particularly those which have an electric motor – require short burst of energy on start-up which is much higher than their rated power consumption. No problem – the Phoenix inverter has industry-leading peak-power capability.”
That peak-power capability is delivered in an 'overload' condition.
If you were to get the 98L Fridge that has the 131kW/Annum use, it is possible that it has a bigger compressor to cope with the freezer box (I don't know for sure). If that
is the case, then I would not be surprised if the 12/500VA Inverter is not big enough either and you should get the 12/800VA unit as a minimum.
You can of course use a non-Victron inverter and go to 1000W for less cost than the Victron 12/500 or even the 12/375 which is too small anyway. there is no reason why you cannot. I selected and recommend the Victron for a number of reasons. Price is clearly not one of those, but I still would not get a non-Victron unit.