Hi Pete. For me the two biggest changes for off-roading are losing weight (the bike not you!) and dedicated dirt tyres. Trouble is that whatever you do will usually make the bike worse as a commuter. The better at the muddy stuff, the worse it will be on tarmac. You need to find the sweet spot in the range of compromises that fits your needs.
The trail equipment sold by our hosts is a good place to start looking for weight-savings. You'll be glad of every pound you shed when you're pulling it out of a ditch - again
For tyres it depends on what you class as "green-lane". At this time of year mine need to cope with all sorts of slime, gravel and boggy grass - even on the main roads! I haven't heard of a trail tyre that would cope with mud without clogging the treads. I use TKC80 tyres and these are amazing at shrugging off everything from deep gravel to deep mud but again, not good for commuting. If you are planning on some gentle forest roads on sunny afternoons then the dual-purpose may work but be aware that at some point you will have to turn back if the going gets wetter.
Softer, longer-travel suspension is a great aid off-road and kinder on the rest of the bike but again this will compromise road manners. Somebody on the forum directed me towards Norman Blakemore for off-road shocks and so far they've been a good buy. I've paired these with the Hitchcock softer springs and 5W oil in the front. The shocks are available in longer lengths, which gives more ground-clearance, but then you need a chain tensioner and swing-arm protectors plus the bike will be twitchy on tarmac with the steeper rake.
Like I said, get a firm idea in your own mind about what the bike needs to achieve and decide which compromises you'd be prepared to accept.
My list -
1. better tyres
2. lose weight
3. softer suspension (even if standard length)
One final word - you are heading onto a slippery slope both physically and metaphorically! Every time you go out there will be some path that you could have taken if only you had upgraded this one bit of the bike. It's a dirty addiction!
I'm sure there will be plenty of others who will chime in on this.
Stuart