From your description, six shots fell within a 35 fps range (2738 to 2773 fps). One shot registered at 2723 fps, or 15 fps below the lowest of the six listed above, and an additional shot registered at 2782, or 9 fps above the highest of the six listed above. Why do you believe either of these two velocities are necessarily outliers?
Of course, it's difficult to prove one way or another without having all the values, but my instinct tells me you simply have an 8-shot extreme spread of 59 fps. Unfortunately, we typically do not shoot the optimal number of shots required for solid statistical analyses. If we did, barrel makers would be ecstatic. If you have a sufficient number of data points, you can effectively make a determination of whether a velocity value is an outlier using distribution [statistical] analysis.
Of course, we normally would like to minimize ES/SD values in the reloading process. One thing you might look with relatively little effort at is whether the cases representing lowest/highest velocities from your shot string have noticeably different volumes. Alternatively, you can weigh them if it's easier, as heavier cases generally will have smaller internal volume. When attempting to determine the cause of a particular velocity outlier, every scrap of information about the loaded rounds you can record may be useful (i.e. case volume.weight, exact charge weight, seating depth, etc.). If something is different about the outliers, that can sometimes make it easier to spot.
On the other hand, we often try to do a number of things in the reloading process to a level well beyond what might be required to prevent affecting velocity noticeably. In other words, we weigh powder to a very fine increment, seat bullets to very exacting dimensions, re-size and trim cases (possibly even sort them) so the internal volume should be fairly uniform. By doing as many steps as possible to a more exacting degree than necessary, what we are trying to accomplish is simply to eliminate these steps as as the largest, or "limiting" sources of error. The largest source(s) of error, whatever it may be in your hands, will have the largest impact on your velocity readings. Collectively, several smaller sources of error added together can have the same cumulative effect as the limiting source of error, but not this is not so common if you're fairly careful and follow good reloading practices. It's usually one or two things (limiting sources of error) that cause high ES/SD values. A list of common causes for high ES/SD might include non-uniform neck tension, charge weight variance, and choice of sub-optimal primer for the powder/cartridge/bullet weight among other things. I usually find choosing the right primer, meticulous brass preparation, and precise weighing of charges is usually sufficient to generate pretty reasonable ES/SD values. Determining the exact limiting source of error(s) can sometimes be very difficult, especially if it's not one of the common ones. A lot depends on how much time/effort you're willing to devote to the problem, but it is usually possible to isolate one variable at a time, test it, and if it's not the problem, move on to the next. It can sometimes be painful, though. I'd suggest trying the obvious steps first to minimize ES/SD to the point you can keep it under 30 fps, or so, which is not enough to be a big issue at 300 yd. In addition to consistent brass prep and charge weight delivery, if you have a different brand or two of primers, you might give them a try with your load. Sometimes switching to a different primer is all it takes. Good luck with it!