AppleScript works for everything except Exchange server emails

Question

Here is the script:
using terms from application "Mail"
          set theRuleName to name of theRule
          on perform mail action with messages theMessages for rule theRule
                    tell application "Mail"
                              repeat with eachMessage in theMessages
                                        set theSender to extract name from (sender of eachMessage)
                                        say "Mail from " & theSender using "Alex"
                              end repeat
                    end tell
          end perform mail action with messages
end using terms from
It is called from a Mail rule. Here is the rule:
It works for every incoming message except for those that originate from an Exchange account.
Here is the interesting part: If I manually "apply rules" by selecting the message and using Option ⌘ L then it speaks the name perfectly. It is only when the mail arrives (by checking for new mail, for instance) that the script does not appear to do anything.
More interesting: The email does get its background color set to Blue. So as far as I can tell, the Rule is being executed, but the script isn't.
Here is the Rule for everything else:
(speakname5 is identical to speakname6 just without the voice "Alex" - here it is anyway)
using terms from application "Mail"
          set theRuleName to name of theRule
          on perform mail action with messages theMessages for rule theRule
                    tell application "Mail"
                              repeat with eachMessage in theMessages
                                        set theSender to extract name from (sender of eachMessage)
                                        say "Mail from " & theSender
                              end repeat
                    end tell
          end perform mail action with messages
end using terms from
If I try to simply use the same Rule for everything it still does not work for the Exchange email account. That is the reason for two separate scripts - it was a troubleshooting attempt.
Why does it only work when manually "applying Rules"?
Is there anything else I can include in the speakname6 script to indicate that it is actually being called?
Here are all my Rules, so that their order is known:

Answer 1

Here is my revised, simply awful, script:
using terms from application "Mail"
          on perform mail action with messages theMessages
                    tell application "Mail"
                              repeat with eachMessage in theMessages
                                        say "script entry"
                                        set AppleScript's text item delimiters to {""}
                                        set theSender to sender of eachMessage as string
                                        set brkpos to offset of "<" in theSender
                                        if (brkpos is greater than 1) then
                                                  say "break position is greater than one "
                                                  set theSender to (text items 1 through (brkpos - 1)) of theSender as string
                                                  if theSender contains "\"" then
                                                            say "the sender contains a quote "
                                                            set AppleScript's text item delimiters to {"\""}
                                                            set theSender to text item 2 of theSender as string
                                                  end if
                                        else
                                                  say "break position is less than or equal to one "
                                                  if (brkpos is equal to 1) then
                                                            say "break position is equal to one "
                                                            set theSender to (text items 2 through -1) of theSender as string
                                                  end if
                                                  set AppleScript's text item delimiters to {"@"}
                                                  set theSender to text item 1 of theSender as string
                                        end if
                                        say "end break position test  "
                                        say "Mail from " & theSender
                                        say "script exit"
                              end repeat
                    end tell
          end perform mail action with messages
end using terms from
The result of all this is the same... a tortured way to extract the sender's name, which works but the results are exactly the same as the other one.
When an Exchange email arrives, the above script speaks "script entry" and that is the last I hear from it. All other emails speak the sender's name just fine. As before, manually "applying rules" after the email is received speaks the sender's name as I would expect.
So it is getting lost prior to "end break position test" but I have no idea why.