I don’t like having a bunch of different powders around. Is there any powder that will work well in both my .270 Winchester rifle and .357 Magnum pistol?

No. Case capacities in these two cartridges are so drastically different, that any powder that might work well in both will not be particularly well-suited to either. The appropriate powder for a given application is determined by a number of factors. Large capacity rifle cases with relatively small bores (like your .270) are best served by fairly slow-burning powders, such as IMR 4350 and H4831.
The .357 is at its best with slow-burning pistol powders such as H110 and WW 296. While a very slow burning pistol powder such as 2400 may be used in the .270 (and most other rifle cartridges as well), it can only be used with very mild, reduced loads. These pistol powders burn too fast to generate much velocity in the .270 before reaching dangerous pressure levels. Economy is fine, but there really is no shortcut to using the appropriate powders for a given application. Refer to the powder burning rate charts and the reloading data table for a
particular cartridge in order to determine which powders are best suited to it.