Good observation on your part that everything pivots at the front screw area, most folks would never know that. The replies you've got above are pretty technical, but are dead on the money for being really good advice.
Resoaking the wood in oil sounds like a huge pain in the a, and if you're not inclined to do it, and the wear is not too much here's some ideas.
Its a little tricky giving advice without seeing the rifle, and in spite of that, lol, I'll toss in 2 cents worth. The pros around should correct me here too if I'm off track.
A)You can make the front triggerguard/screw area clamp onto the wood by carefully/slightly shortening the bushing that the bolt goes through. There is a proper method here on this forum, and if you want to do this, someone will point you.
b) If your front screw is clamping the trigger guard firmly to the wood when tightened, and you can make an up and down movement happen with the wood at the back of the trigger guard, then you may have something that can be fixed with simple stuff, by packing either side of the trigger under the trigger guard, or on top of the draws. Some enfields develop this looseness over time due to wood shrinkage. Sometimes shooters want this area tighter on the wood too for improved accuracy even if not too loose start with.
First, go to the front of your rifle and make that movement at the rear happen. Enfield no4's have a floating barrel and it should be pretty much centered where it exits the front hand guards/fore end. If the looseness lets you push the barrel to the bottom of the hole, then your wear and tear is at the top of the draws. If the looseness lets you push the barrel to the top of the hole, then your wear is at the bottom of the draws. If you can do both, then you have wood shrinkage that has affected both areas.
Turn the rifle upside down and go to the back of the trigger guard; target shooters sometimes put thin strips of stiff card about one inch long on both sides of the trigger on that little ledge that the guard presses against. This takes up slack that lets the barrel go up at the front. There can be 3-4 layers here sometimes. A proper fitting trigger guard should match to its two screw holes and lay flat in the wood, without any leverage or pressure being applied. In your case tho you need to fiddle everything a bit until the slack is taken out, sometimes it will take some shooting to help it settle down.
If you're taking up slack that lets the front of the barrel go down, then you have to pack on top of the fore end wood where it touches the receiver, the draws area in one of the pics shown above. This will involve taking the fore end on and off a few times and packing it more or less, until you get it right. One of my rifles had thin brass sheet cut into patches the shape of the wood, to pack it up. The pressure of assembling the rifle usually squashes all these shims into place and they mostly stay put during future dismantlings.
(There is a set of pics here on this forum about enfield accurising techniques that show all of these packings/shims in place on a couple of fultons target rifles.)
Getting the looseness out before you go shooting is crucial.
Recoil forces on a fore end thats not clamped tightly by that front screw will, and I mean will, split the wood in one shot, sometimes as far as the front band, with that front screw behaving like a wedge. This also means that pieces of split fore end wood are coming backwards, very close to your eyes, don't shoot without safety glasses. I can vouch for all of this from experience, and I got lucky without getting the stock in my eye. The left and right sides of the fore end came back behind the wrist where the serial number is, thats far, and way too close.
However, get it basically right and you're in business. There's also plenty of enfield videos on youtube and perhaps there's something on this subject, its growing all the time.
Milled micrometer enfield no4 mk1 sights are $20 or so from springfield sporters and are easy to fit right on where your flip/flop is, with the same pivot, spring etc etc..