I tried to read most of the comments to avoid repeating what's already been said. There's a lot of good advice out there already, covering tires, suspension, and riding technique. I'll add a couple things, simply because I didn't see them already mentioned or explained the way I would say it. So here they are...
The problem with the front end of the V-Strom is actually a combination of things including too soft of compression damping in the forks, having so much weight on the front end, having such a wide tire in front, and quick-turning steering geometry. Fixing one of these things alone won't help greatly. Fixing two of these will help some, and fixing three will help quite a bit. There's not much you can do about the heavy front end, with that V-Twin engine hanging there. You can generally make this better by keeping your weight back on the bike. There's been plenty said on that subject already. As for the forks, even with Gold Valve emulators, which most of us set up for combined riding, V-Strom forks will be challenging to ever tune in enough compression damping to handle soft sand. If you did tune the forks that way, you wouldn't like them anywhere else. You would probably get beat up by highway weather strips.
[Sidebar story: I had a 2016 KTM 300 XCW which I dearly loved riding in the woods, and even in places with course sand (actually tailings from a mining operation). I rode an enduro in Northern Indiana, which happened to be adjacent to Naked City nudist camp (but that's another story). It was deep, soft, sugar sand almost everywhere. It was the worst experience I ever had on my trusty 300. I was stopped trying to catch my breath and someone pulled along side to check on me. They advised me to crank in my compression dampers... a lot! I went in about 4 clicks, which helped the front end stay up in its stroke. That made it much easier to keep my weight back, because I wasn't fighting nose dive anymore. The course still sucked, but I was able to regain steering control, which I didn't have before.] As that knowledge applies to the V-Strom (at least one my Gen 1), the best way to compensate would be by cranking up the preload. That would at least reduce some of the front-end sag.
The wide front tire is also a problem in sand. Disregard the tread design for a moment and just think about the amount of surface area on the tread and sidewall of a 110/80-19 tire. There's a reason dirt bikes typically run a 80/100-21 front tire - it cuts through off-road terrain like a knife. A difference of 30 mm is well over an inch of addition width. First, the width is trying to push, rather than cut, through soft material. The width of the tire makes it want to ride up on top of the material, which is providing a lot of resistance. The weight of the bike prevents it from happening; it's constantly fighting itself, resulting in a bucking motion up front. Then, when you turn the wheel the least little bit, the resistance of the material pushes on the newly-introduced, even-greater surface area of the tire sidewall. Without a steering damper, or a set of Herculean arms, the front end is headed to full-lock right now! I don't know if you have ever searched for information about installing a 21" front wheel on a V-Strom, but there are quite a few people asking about it. There are very few people who have a credible answer. And, no one I've seen has an off-the-shelf kit for installing forks off a DR or RM (if you want to keep it in the Suzuki family).
And finally, there's the quick-turning steering geometry of the V-Strom. One my Gen 1 DL650, I have 1/2" of fork tube (measured to the bottom of the fork cap) extending above the top triple clamp. This provides a good balance of lively cornering on twisty roads, and reasonably good straight line stability at highway speeds. I never have headshake at speed, but I also don't trust it to ride it no-handed. Dropping the front end (raising the forks higher in the clamps) makes it quicker turning. Raising the front end (dropping the forks lower in the clamps) makes it more stable in a straight line. If you are going to spend the whole day in soft sand, it's probably worth taking the time to drop the fork legs; even a quarter inch might help. Again, just like with tuning the damping, extreme adjustments tend to hurt versatility.
While I'm talking about forks, it would be a good time to mention the use of a fork brace. Because the forks aren't real beefy, and because they are traditional right-side-up style, it's understandable that they are going to flex. The right and left can move in and out (to and from) each other, AND they can flex forward and backward opposite of each other. The result of the later is front wheel wobble. A fork brace clamps the two lower legs together as a more solid single unit, helping them stay parallel. I noticed a huge difference with my bike's stability in the wind, especially strong side wind. If it makes a noticeable difference on something (wind) that pushes on the whole bike and not specifically the front wheel, imagine what it can do resisting something (sand, rough ground) that does push on the front wheel.