What Delbert is offering may be your best bet. Carpenter never carried the stuff in less than 1/2" thickness (well perhaps before I was born). Crucible only sells theirs in rounds, I have come to enjoy 1- 1/4" rounds for the price savings and the massive squashing I can do. Admiral does have flats but the sizes have already been discussed here.
With .55 to .60% carbon 5160 gains its impact strength from a healthy dose of proeutectiod ferrite (not as much carbon) and obtains its hardness with a helping hand from chromium. L6 obtains its impact strength from nickel fortifying the ferrite matrix, and with .75% Carbon it would obtain a healthy hardness all on its own but is also helped along with Chromium. L6 has significantly higher impact strength than 5160 at higher hardness and will hold and edge longer, althoough there are other steels that will hold an edge longer than L6. Some L6, such as Crucibles, also has Mo, which will have very marked effects on its heat treating.
I abandoned 5160 years ago in favor of L6 but that is not saying that 5160 is inferior as there are always trade offs. The biggest plus you will be sacrificing in such a switch is easy working with simpler tools and techniques. 5160 is a great beginners steel beacuse it is very hard to mess it up, and it is very easy to work it with the simplest of tools and techniques. L6 may require a little more skill and the ability to properly heat treat it, particularly pre-heat treatments before machining and grinding.