Should I start again?

So, I load up some rounds to test.

30-06 Hornandy 3045 BTSP 165 g
IMR 4350
I make loads at 50/50.5/51/ and so on to 55.5 g
Cases are 2.488 and col is 3.228
The wind was about 15 mph from behind with some gusting. It was about 85 or 90 degrees.

Out of the 12 3-round groups, two are sub moa. The 51 g and the 54.5.

The vast majority of the groups had 2 of the three rounds 1/2 inch apart with the 3rd round about 1 1/2 inches away, some farther.

So, I figure if it was the wind, the rounds would be all over. I also am confused by the two groups that shot sub moa with the powder difference.

I'm new to reloading so any advice would help. I did let the gun rest between groups.

I'm assuming you have the sporter barrel, correct? How long are you waiting between shots? I have a Savage staggerfeed 30-06. I'm loading the 165 gr Sierra BTHP in Lake City match brass, BR2 primers over IMR4350 with charges similar to yours. My OAL is just enough for the rounds to fit the magazine. So far, waiting a few minutes between shots, I've been able to put three into .678" at 100 yards for a few groups. My worst group was 1.1" towards the end of my range cession. I wait almost 10 minutes between 3 shot groups and let the barrel cool in the shade of my truck bed cover (90 degree plus temps in central Georgia and a blazing sun heating the barrel when it just sits in the sun). The previous owner painted my barrel flat black so it really soaks up heat from the sun. I pour cool water on the barrel, wipe it down, before sitting it in the shade, seems to help the "cool down" to be quicker.

Yes, I think it's a 22 inch barrel on a 111. I'm waiting 5 to 10 minutes between groups. Not totally cool but a lot cooler than just shooting them all.

Are you using some kind of wind flag? (It don't have to be fancy a few pieces of surveyors tape on a stick placed at about 3 yardages will be a big help.) Shooting without them is worthless, it is kind of like driving a sports car without a tachometer.
You mention that the wind was behind, the difference between 6 o'clock, to 7 o'clock, or to 5 o'clock will be huge, and depending on wind speed, it will magnify this even more.

What are you resting the rifle on? Not having a solid rest, will also have a big affect on accuracy. (Again don't have to be expensive, good old sand bag bags work well.) Trying to minimize a group without either is running around in circles. I would also say that unless the shooter is very highly skilled that they have a part in making the group size. The 30/06 can be a highly precision round, but do to the recoil it can also cause flinches, and other bad habits, that will show up on paper. The light weight of a model 111, doesn't help in the recoil department. You should be able to get that gun to shoot 3 shot groups at under 1/2 inch, at 100 yards all day long. I don't wait between shots, when you wait you get a different condition (Wind direction, speed, light, mirage, ETC) to shoot in, and it will almost never be the same when you shoot the 2nd or 3rd shot. Let the barrel cool down between strings. (example shoot 3 shots then let the barrel cool.)

One last thing on the gun, is the scope paralax free? Most hunting scopes don't have an adjustable paralax feature, and they can very one where they are paralax free. The way to check for paralax, is look through the scope, and move your head around. When doing this if the cross hairs, or the target jump around then you have paralax.

When shooting you will typically find 2 powder loads that will shoot the best, The reason why is you have found the frequency nodes of the barrel. (deals with harmonics.) You will usually find one low and one high, most shooters prefer to shoot the high node. After you have found a powder charge that is good, then you can play with seating depth, and tune it in a bit further.
Try different powders, and bullets, I look for a load where the three shots go into the same hole. (Or close to it.)

Im working up a load now for my .308, and its interesting how a few grains of powder makes such a big difference. My last trip out I loaded up some cases with 41.5, 42, 43, 43.3, and 43.6 grains of varget (165g hornady sst) The 43grain load shot with 4 of 5 rounds touching, the 43.3 grain load shot into just over an inch, the other 3 loads were between 1.5-2.5 inches.....

In other words, thats completly normal. Thats the whole reason we try different powder weights when working up a load, because in any given gun, using the same bullet, brass and primer, you can have large differences in accuracy with just half a grain powder difference..... or even less... in mine, the 43.3g load went into just over an inch, while the 43.6g load was over 2 inches....