I’d keep the inverter. In a year or two you might decide to buy a small van and do a conversion. 1100W will just about run a low wattage microwave, as the 1100W bit is usually the amount it can supply constantly and it will probably have a surge limit as well that is higher. The actual power on a 700W microwave is about 400-500W higher, if you shop around. The 700W Russell Hobbs ones tend to be pretty low on actual power needs, so some might use 1100w. Or you could go with a custom microwave. I saw one on Amazon that uses 320w, aimed at people with campers. But cooking time goes up on something like that.
As far as the portable bit. if you know your AC charger uses 150w, you could pick up a smaller inverter, a smaller battery that would still charge from a VSR, cobble something together (50Ah Battery, Fuse Box, Inverter (or DC Charger) in a rucksack). It would give you field charging capability and a power supply if you need to make in the field repairs. Weight wise, less than 20kg, a Lucas 50Ah Mobility AGM battery is about 15kg, fusebox, smaller inverter, maybe an XT60 connector, USB charger socket, cigarette lighter socket, maybe a kg. So 16kg, plus whatever your drone weighs and any spares you carry and other tools. So maybe 16kg + the drone kit. That assumes you want to hike miles off the beaten track then fly your drone for a while.
But would it be cheaper to buy more drone batteries and charge them at home?
I can see use for both.
I started to build one based on a 34Ah AGM for in the field Lipo charging. Then when i got back to the van, plug a lead into an XT60 connected to a secondary charging system, allowing it to access solar and vsr charging (on a sunny day it would charge a 50% discharged 34ah battery in a couple of hours max). I realised I don’t fly miles from where I park, so it was pointless. Also i could charge 20 Lipos and just take them with me. I have not been to a site where I needed more than 15 Lipos. 
So I would say in car charging, yes. in rucksack charging, only if you say plan to park up at the base of a mountain, hike up it and need on-the-fly charging capability, or maybe a steady power supply for a long range base station, flying a 10 mile round trip. Apart from that, go back to the car and recharge. 