The only thing I can think of offhand is the three quick beeps could be from either having FAC/CMC enabled on the route patterns or MusicOnHold is being invoked by a quick hold (network-hold).
You hear 3 quick beeps for tone on hold (no music file or when MOH server is not running) when someone is put on hold, or a network-hold is done by ccm for some reason. As a quick troubleshooting/isolation step, you could set the tone on hold timer value under call manager service parameters to 200000, this disabled the 3 quick beeps at start of hold.
Are there any partition/region differences, mtp, etc for where these route patterns are going? Overlapping dialplan and it's trying something else also?
A CCM Detailed trace would give the details on what is happening and causing it.