David, sorry to hear of the LiDAR costs, however that may leave the field open for a 'proper' geomagnetic survey...
From your description of your magnetometer I'm not sure that what you had is really what you'd want for this sort of work? The style of gradiometer I'm thinking of will record data that you then download to a computer and analyse - often producing a '3d' relief map of what has been recorded. Typically they use two or more single or multi axis magnetometers (which may be housed in a tube, but it would be unusual to find the batteries also in that tube).
These have been used to great effect in archeologic surveys, but like the unit you used they will be extremely sensitive to nearby ferrous material (the operator should ideal wear gumboots, no watch or belt buckle etc), and it's important to conduct an accurate grid search. I think that with the right sort of gear and some lateral thinking the latter may be able to be addressed to some extent with modern equipment and concurrent GPS data (realising the nature of the terrain you're working with).
Alternatively I see no reason why a reasonable sized drone couldn't carry a suitable gradiometer and be programmed to fly a grid pattern, thus alleviating the terrain issue. I have an idea I've seen someone else here mention this too but I'm aware that there are such things in a commercial field (Sensys comes to mind) although I am uncertain of their effectiveness for this particular search you have in mind as I've not worked with them directly and am unsure if their units are a single magnetometer or a gradiometer.
However taking this one step further I'd suggest that in any event it would be reasonably simple to test the effectiveness of any such system well before trying it out in PNG - place a motor on the ground in a field and/or the side of a hill, run a standard grid pattern from a specified height and chart the results. This should give an idea if it would be suitable for what you need, and/or what could be changed to make it work or improve it etc.
Obviously they do have a cost but it I expect it would be somewhat less than what you've been quoted for the LiDAR survey, and you may find a company or individuals who are able and willing to assist more easily in this space than in LiDAR.
Unfortunately I don't have direct connection with any company that could help you, but I have some experience of the technology (I have built my own mag-gradiometer) and could possibly give you a few leads to try if that was useful - perhaps best to establish contact via a PM if you thought it worthwhile.
Otherwise I trust you will be able to find another suitable, and hopefully successful, angle to approach the search from.
FP.