The cleaning rod trick is the surest way. Let us know which model Remington you've got and we can tell you what the twist is supposed to be. FWIW, factory 700's in .223 are almost always 1-12", unless the rifle is an LTR, PSS, VTR, or has an aftermarket barrel.
If that is the case bullets 60 gr. and under are the options likly to work for you. A faster twist is a different animal all together.