Ok, change of plan - that original reverse protection circuit does work - once you realise the MOSFET is being used 'upside down' which for a normal transistor would mean instant destruction but, counter-intuitively, is apparently OK for a MOSFET. The difficulty is finding a P-Channel MOSFET with a turn-on voltage < 1.5v, Jaycar have nothing and Mouser only 1 (IPP120P04P4L-03) but we can be clever and turn the whole circuit 'upside down' and use an N-channel MOSFET for which there are many more choices... though none from Jaycar, but plenty from Mouser, and my pick is the cheapest one SUP40012EL-GE3 at AU$3.31

Here's the circuit - note the MOSFET is in the battery - lead but that doesn't matter as the whole thing is floating... and only 1 component!



And just to show it works, here's the output from a simulation... battery volts go negative - nothing goes to the board, goes positive, board draws current...



Here is how you wire it up...

 

Following that, I wondered if the full bridge would be possible and it is, though you need 2 p-channel and 2 n-channel mosfets.

 

Ok, change of plan...

YES!!! I got back home last night and was searching to find this post to say just that! This is a simple well used circuit recommended by none other that Bob Pease. I almost used it once but did not have the time to test it, and probably would not fit on the small board footprint once adding components for the higher input voltages (not an issue here).

Do check the turn on voltage if substuiting for that SUP40012EL. It needs a Vgs(on) below the battery voltage, which this has but many do not.

However... is even this really necessary? The mechanical solution is to use a comnnector that cannot go in backwards, such as the ubiquitous 5.2mm barrel type. (Note the "9V" battery type does allow reverse polarity to occur, you just can't snap it in that way) (but your circuit is already fried).

 

YES!!! I got back home last night and was searching to find this post to say just that! This is a simple well used circuit recommended by none other that Bob Pease. I almost used it once but did not have the time to test it, and probably would not fit on the small board footprint once adding components for the higher input voltages (not an issue here).

Do check the turn on voltage if substuiting for that SUP40012EL. It needs a Vgs(on) below the battery voltage, which this has but many do not.

However... is even this really necessary? The mechanical solution is to use a comnnector that cannot go in backwards, such as the ubiquitous 5.2mm barrel type. (Note the "9V" battery type does allow reverse polarity to occur, you just can't snap it in that way) (but your circuit is already fried).

Yes, I was too quick to dismiss the original circuit and it took me a while to get my head around the fact that the MOSFET is 'back to front', ie p-channel drain to +ve!

But it is quite difficult to find p-channel MOSFETs that will handle the peak current required and still stay fully turned on at Vgs = ~3v. Although there are a few, they are not stocked by Mouser or Element14. It was a while before it clicked that we weren't constrained to the +ve rail and could use an n-channel and then we're almost spoilt for choice, but even so getting the right balance between Vgs, Rds(on) and Id is a bit tricky...

The mechanical issue is that the 18650 can easily be inserted in the holder either way round, its not a connector problem. They don't have as big a +ve end lump that a dry cell has, although I've never managed it myself.