Hi Ratcatcher
Hope you get the good news today - It feels like it's taken a long time.
Remember brambles aren't your enemy! I think paths through are the way forwards - you don't need to be able to stand on every square inch of land, but of course it's perfectly reasonable to want access. How dense is the canopy of your woodland? The main thing that determines how thick and vigourously brambles grow is the nature of the canopy above them - and of course the soil type, but canopy is king. Could you describe the make up of the canopy as it is now? The thing is that frankly it would be just nuts to attempt to control bramble over a large area in any way other than focussing on the canopy - they will just grow back and the task wil be never ending.
Depending on the history of management of your wood brambles may be either an artifact of that management - recent (i.e. less than the last 10 years) thinning/overthinning, or perhaps a large felling 25-35 years ago. If that's the case the vigour of the brambles will decrease dramatically over the next few years - you have to actually see/experience this happening at a wood to believe the extent to which it happens! The other situation is that you have the type of woodland (I'm not a big fan of the system but have a look at NVC woodland classification tables) where bramble is an important ecological component. In which case, unless your of the "I'm the king of my kingdom an I'll force it to be however I want it types, then perhaps pathways through and a few large clearings might be the most ecologically sensitive compromise.
Seasonal standing water as you show in the picture causes no problems and again has many eclogical advantages - I'd suggest just letting it be and seeing what happens naturally to it.
As for making a dead hedge of bramble that just sounds like the most awful way to spend your time imaginable - a task to be reserved as punishment for society's most evil criminals!
Perhaps you might also stay mindful that it's March before the end of the week and that bramble thickets are where many birds wil be making their nests - in most cases they will already have decided on sites and territories based around them.
Of course the above are only suggestions I'm not telling anybody what to do!