Re: Inverter or no inverter?
Two options as you have identified.
1) Get a DC-DC Converter
2) Get an Inverter and use your existing power supply
Pros and Cons of each.
Pros: Efficiency - reduces conversion loses going from DC-AC-DC. (Note that there ARE still losses converting from DC-DC though)
Cons: Expense - need to buy a DC-DC converter
Cons: Flexibility - if you change device, you probably need to buy another converter
Pros: Flexibility - you can plug in any 240V AC Device (within power limits) you want using existing AC power block. Change lapop, have two different laptops. Use for other stuff than a laptop. Doesn't matter.
Pros: Expense - once bought, doesn't need changing if devices change
Cons: Efficiency - DC-AC-DC losses higher than DC-DC losses
You can get an Inverter for less money than a pre-packaged DC-DC Converter and that inverter will also work with any laptop, same as your 13A socket at home works with any laptop.
Inverters tend to have around 85% efficiency, so you will use say 15% more battery power compared to a DC-DC Converter while it is plugged in. If you use the inverter when driving to charge the laptop, then that extra use will be made up by the alternator/split charge system.
If you have just one specific need and would be delivered by either an Inverter OR a DC-DC converter, then the DC-DC Converter is the more effective option. If you think is is likely you will need multiple DC-DC converters (more devices, changing devices) then the Inverter can be a better option.
I use both in my Campervan. I have battery chargers for tools, electric blanket, rechargable toothbrush, laptop, plus various other stuff. If I was to get DC-DC converters for, or source DC versions, of all those things it would cost loads of money whereas a single inverter will do the job.
However, I also run an Amazon Echo in the van which stays on 24/7 when I am away. That uses a tiny amount of power and an inverter being on just for that would be incredibly inefficient, so I made a DC-DC Regulator (Converter) for that specific device.
Horses for Courses, but don't dismiss the simple option due to scaremongering tales of inverter inefficiency.