I do not know about these micro-inverters, but normally the grid tied inverters cannot be used stand-alone. They rely on the grid to keep the voltage constant. Essentially these inverters are current sources.
Mentally I also had the same problem. Having a roof full of solar panels and when you really need them they cnnot be used.
I see you also live in the Netherlands, so power outages are not a big issue. Therefore I also did not want to invest a lot in an off-grid setup.
I generated my own solution by using a 24V Meanwell DC power supply directly attached to the panels (a switch and fuse in between). A lot of these can just be fed from directly from DC, no AC needed, this possibility is even stated in the manual, so there should be no safety issues as well. I used a small opamp circuit attached to the sense input to generate a CC/CV mode. At low battery voltages it will limit the current to the batteries. When fully charged, it will remain at a constant voltage.
I specifically avoided an MPPT charger, as I want to be able to have the input in parallel to my normal grid-tied inverter. having two separate MPPT controllers in parallel did not seem like a good idea.
For the batteries I used lead truck batteries. These are replaced in garages at regular intervals. Most of them are good enough for solar panel use. For just coping with power outages, no fancy batteries are needed, as (hopefully) it will not go through a daily charge/discharge cycle. It will only be used incidentally.
I also experienced, that big truck batteries can easily be exchanged at the local car junkyard for about 10 euros. They are only interested in the scrap metal, so no difference to them if you exchange bad ones for newer ones.
After the battery I just use a 600W inverter to generate the mains voltage. I do not need the full output power capability of the solar panels. I need enough to drive the fridges, the central heating pump, etc. The inrush current being the dominant driver for these motors I chose an LF inverter.
This whole setup only costed me 160 euros.
In case of a power outage I could use extension cords to critical applications. However in the Netherlands, there is hardly any need.