I don't know what part of the world you are living in, but 350 yards is a long shot on a fox. I've killed a lot of foxes over the years in Mexico, Ca., and Arizona with a 243. Needless to say, the 243 is rough on a fox until the yardage is beyond 200.
When you skin the hide off a fox, you don't have much of a body as far as size, which is very surprising. For this reason, I would suggest a fast load.
I have shot the 60g Sierra HP at 3800 with amazing accuracy at 3800 fps using a max load of Win 760 in several 243's. I think that the king of all loads that I found in several 243's has been the 80g Sierra BT Blitz bullet loaded with 39.0-41.5g of IMR 4064, Rem Case, with Fed 210 primer at 3450 fps+ depending on the rifle. This load is very flat shooting and holds up good in the wind and knocks the dickens out of anything that you shoot with it.
For some reason, the bullets in the 90g range rarely get more than 3100 fps with great accuracy and their trajectory makes range estimation on a fox at 300+ tricky. When preditor hunting, you rarely if ever get the chance to use a range finder, you usually have a nano-second to estimate range and get the animal in your crosshairs. For this reason, an extremely flat shooting bullet is needed.
You mentioned that you wanted some wind bucking ability, and I did not mention the 70g bullets, but they are usually extremely accurate with Max loads of IMR 4064 and Win 760.
In my years of shooting the 243 where you have to shoot quick shots at guestimated distances, the 80g bullet pushed to the hilt seems to do the best job of not hitting the animals low in the stomach, therefore not dumping all their guts on the ground. For many years, I shot the Sierra 85g BTHP and the 85g Spt, but when I went for the 80g Sierra, I quit unzipping animals at longer distances.
The 80g Sierra Blitz at 3450 seems to be one of the perfect varmint rounds out of standard factory rifles due to it's energy dumping ability and good BC that leads to some wind bucking.
I avoid using poly tip bullets on coyote and fox because often you are shooting at them on the move, and if that poly tip bullet hits a twig, the bullet will blow up.
The 80g Sierra Blitz did a much better job on coyotes, bobcats, and foxes than the 85g Sierra's of any variety. The 80g Berger did an ok job at closer ranges, but there was not much expansion at longer ranges.
The 80g Blitz also does not have a lot of bearing surface which equates to MUCH less copper in the barrel if you happen to get a factory barrel which is less than perfect.
If you are saving pelts on foxes, then I had good luck with the 100g Hornady SPBT loaded with 42.3g of IMR 4350 with a WLR primer in several Rem sporters. It is not a flat shooting round as are all of the heavy bullets in a 243, but will give you killing performance and excellent accuracy.