I've got the plain-old Remington 700 Stainless Synthetic Mountain Rifle. It should perform similarly to your rifle, however, because both use the same skinny stainless steel Remington factory barrel (which is truly excellent, I might add).
Like Tod says, this rifle is good for 3-shot groups before it starts to open. That's simply a product of the skinny barrel heating up much more quickly than a heavy barrel would in the same situation. This is not a problem because it is a hunting rifle, not competition rifle.
My Remington is generally not too finicky, but so far I've found that it likes 165 to 168-grain bullets the best. I'm currently using 64.0 grains of Vihtavuori N560 with a 168-grain Barnes TSX, in a Winchester case, ignited by a WLR primer, and I'm solidly cracking 3,000+ fps over the chronograph, with the first three shots landing inside 1 inch at 200 metres (i.e., 1/2 m.o.a.). My previous go-to loads have been 62 grains of Reloder 22 with a 165 Nosler Ballistic Tip or 165 Hornady and 50 grains IMR 4064 with a 180 Partition (the latter is fairly stout but is safe in my rifle and is listed in at least one or two books).
All of the usual classic .30-06 loads have worked well, but I've found that my Remington has a "slow" barrel and generally never achieves "book" velocity (with the notable exception of the Vihtavuori load mentioned above -- another reason why it is now my load of choice).
I've also found that the Remington has a looonng throat. I'm seating the 168 TSX to an overall length of 3.400, and the Ballistic Tips go even longer. Thankfully, the magazine box on this action is long enough for magnum cartridges, so length is not a problem. Have you gauged your throat with a Stoney Point? I'd be willing to bet you have a jump upwards of .050" with the Interbond loads you've described. On the other hand, if the loads work, there is no need to fiddle with them.
The final comment I can make is that this rifle needs to be properly bedded. Obviously, the action needs to be bedded in the usual spots. My rifle has the factory "Tupperware" stock, so conventional bedding compounds have difficulty sticking. I ended up using the heavy-duty version of automotive Bondo called "Bondo-Glass". It has worked well for several years and really kept the action mated to that flimsy stock.
The other thing that I've found to be an absolute NECESSITY with this rifle is to bed a little pressure point in the forend. Nothing I've ever done to this rifle improved accuracy as dramatically as putting a bit of uniform pressure under the forend. This is probably due to the skinny, whippy barrel combined with a flimsy Tupperware stock. I simply bedded the area with Bondo-Glass then covered the bedded part with two layers of electrical tape, so the barrel is not resting on something hard.
The factory stock had two little ridges built in to supposedly place pressure on the barrel at the forend. Unfortunately, these little points did not provide uniform pressure, so I sanded them out and replaced them with the blob of bedding material described above. The result has been magic.
These are just a few of my comments about this superb rifle. I'm sure many others will chime in.
