One reason for this misalignment is the secondary may not be square to the focuser. The secondary can be rotated around in the spider, and everything may look OK for the laser, but the tell tale sign is the mirror is not centred and the stars have little tails, all that you are seeing.
I had this problem too. Took me a while to figure it out when the laser was saying everything was "OK". I wasn't using a Cheshire either, and it made things worse.
If the cross hairs of your Cheshire are busted, you can is still us it to work this out. The cross hairs make things easier but not essential.
I am guessing that your Cheshire is like one of these?
If it is, let me know. I can work out a plan to help you out. There's a couple of ways to do this.
Alex.