I may be out of date.. are people still manually updating the SHA values in XComGame.exe after editing any of the .upk files?
There's no need - it looks like the game loads each pack file and then searches for the given name in that table, and calculates/compares the SHA if it has an entry there. If there is no entry, it doesn't care. This means you can just do a one-time edit which trashes each of the names in that table, and XCom will never compare any of them again.
Note - I only tested this on the entry for 'XComStrategyGame.upk' in XComGame.exe - I changed the first letter to a 'c' and now the game doesn't care about that file's hash.
You don't need resource hacker for this one - the strings for each pack file only seem to occur ones in the executable, so just load up your hex editor, search for the pack file you want to edit, and trash some of the characters within the string.
LMK if this isn't working for anyone else, the next step is to find the function that actually performs the lookup/compare, and force it to return 'true'.