NAC. That's right, absolutely NAC. Electrical question

[John Larson]

So I have this former customer, a charity case, pretty much, with a 
sleeping/breathing problem.  He lives in a 1970 VW bus with only 
occasional access to 110v power.  He uses a respiration helper device 
when he sleeps.  I have the label for the power supply (which has a 24v 
output at 3.75A), and I need to figure out what kind of load that'll put 
on a 12 battery through a 400w 90A inverter.  He already has the 
inverter so we want to try to use it.  I'm planning to install some kind 
of battery isolator, possibly a Ford starter relay (of which I have a 
number) activated by the KOEO position on the ignition switch.  If it 
would be better, I can purchase a dedicated component.  I'm planning on 
using a deep cycle battery and keeping it charged with the alternator 
(and possibly a solar panel, if necessary).  I know there are some of 
you that can do the math while walking and chewing gum, so this one 
should be a breeze!  I'm not one of those people ...................  
Would it be better to just use a 12vDC>24vDC device and forgo the 
12vDC>110ACv>24vDC?

Cost effective way?  Best way?

Thanks!  John