I'm working on getting 140 grain Berger VLD's to shoot decently out of my 6.5x55 Sweede. I got so so results using H4831sc and am now trying some H4350 with slightly better results. Any suggestions would be appreciated.
It's a 1 in 8 twist barrel

I have always thought that the 140 was the best weight for that cartridge and a powder with burning rate similar to 4350 the best choice.
You should also match chamber and case ! European rifles and chamber require European cases [. 479 head] American rifles need American dimensions SAAMI, .473 head dia !
Always known as an inherently accurate cartridge ,if everything else is ok it's easy accuracy. Mine is custom with 1:8 rifling and better than 1 MOA without even trying !

And we come to the very real possibility that your rifle just doesn't like that bullet.

I'm not sure how much help I can give, my experience is from working with a 9.5" twist barrel and 140 grain Sierra Match kings.
My rifle really shoots 140 Sierras at or just under 2750- 2800 fps with IMR 4350, 3.03" OAL.
I am using Speer brass and some S&B brass and can't tell the difference.
In your shoes I'd push that bullet around 2800 and play with the seating depth, if I recall Berger has an in depth description of seating depth and accuracy on their website.

You should try seating the bullet to .010" off the lands, regardless of whether it will load into the magazine just to see if it shoots better. VLD's can be very touchy about jump. At least then you know if you need to give up on this bullet. If it shoots, but won't load into the magazine then I would give the Hornady ELD-M, or ELD-X a try. If neither one of them shoot, would give that barrel a long hard look.

Here are the basics on how I play with seating depth to find a load or fine tune one.
I normally load for hunting rifles so magazine length is critical so basically that's where I start, if your maximum magazine length puts you into the lands then start .010" from the lands
Load 5 rounds of the longest that will function through your magazine (or .010" off lands see above)
load 5 rounds seated .040" deeper than max magazine length.
Load 5 rounds .080" deeper than max magazine length.
Load 5 rounds .120" deeper than max magazine length.
By shooting these 4 five shot groups at least one should show you what it likes and fine tune the depth in or out from there in .010" increments to hit the sweet spot.
If this doesn't work sometimes you must drop that bullet and move on to something else.

Getting close to lands is not really an option. The mag is long enough but throat is too long. The bullet is only about .090" into the case when touching the lands. I have tried moving the seating depth by .040 at the time and a 3.075 over all length seems best. On last tripto the range I shot a 10 shot string at 300 meters and got .67 moa using 43 grains of H4350. 44 grains was not good but things tightened up at 45 grains. at 45 grains there were no traditional pressure signs I may try moving up a bit more in 1/2 grain incements