Unfortunately, iOS doesn't allow background actions except for a very limited number of cases, so you'll have to have Keychain opened to sign transactions.
Damn...
Isn't there a trick to go against the locking mechanism, such as maintaining the phone app on focus (never hibernate)? I know this will rip off the battery but for a necessary evil (and could be an iPhone-only option.
To consider maybe, but needs more user feedback. =)