Welcome to the Forum!
Shooters that do not reload really only have the option of testing a wide variety of commercial ammunition in the hopes of finding one that shoots well out of their setup. Sometimes this approach works, sometimes it is less than satisfactory. Even commercial ammunition preps using the same bullet can vary widely in terms of velocity and pressure between different manufacturers. Further, commercial ammunition preps are typically not held to the tolerances that hand-loaders consider routine. If you like surprises, try measuring CBTO on several rounds of commercial ammunition sometime. Most decent brands of commercial ammunition are formulated to shoot reasonably* well out of a wide range of different rifles, rather than very well out of a particular rifle. So there is a certain amount of luck involved when you find a commercial ammunition that shoots really well out of a given rifle. The more types/brands you test, the better the odds of finding one that shoots well.
There may be a number of reasons your rifle is not responding as well as you'd like to the various commercial ammunition types you have tried so far. The triangular barrel shape is only one of them. The factory chambering work and the inside of the bore may also be contributing factors. There may be a few others such as the stock and bedding of the action that may be more difficult to deal with in terms of precision, even using hand-loading. Regardless of the reasons, by hand-loading with a quality bullet or two, as well as an appropriate powder and primer, you can tune the loads to adjust and compensate for some of these adverse factors, at least, as much as it is possible to do so. With commercial ammunition, it is hit or miss as to whether you find one that shoots really well. The more types/brands you test, the better the odds, but there is still no guarantee. In fact, there is no guarantee even with hand-loading that you will end up with a very accurate/precise load, largely dependent on the true underlying cause of the poor precision. Nonetheless, the odds will be more in your favor as you can test incrementally and select optimal load parameters in a way that you are unlikely to achieve with commercial ammunition no matter how many different types/brands you test.
Your plan of shooting commercial ammunition this fall should work as long as you are willing to accept whatever accuracy/precision you can get until such time as you start load development on your own. Given the barrel twist, you might want to give commercial ammunition with bullet weights in the 175 to 180 gr weight range a try and see if one behaves any better for you. I have fired some commercial .308 Win rounds out of a custom F-TR rifle I have and been pleasantly surprised at how good the precision actually was (~0.5 MOA at 100 yd). The two that worked well were Federal Gold Medal Match w 175 Matchkings and Federal Fusion w 180 SPs. There are a few other commercial .308 Win offerings available with bullets up to the 180-185 gr range.
Good luck with it!
* - defined by the end user, not standardized