They are a pain, those stoves should be fitted with a access door on the flue pipe. Then there would be none of these problems.
Also, you shouldn’t really be sweeping a liner with them rods, as it *could* get caught on the liner and shred it. Also you should have a ball on the top of the brush to stop it getting caught and shredding the liner also.
Your options are:
A- fit a flue pipe with access door, and sweep with your rods and risk damaging the liner.
B- get a sweep out, but check they have either power sweeping (with a 6 inch whip, without the ball on top, they’ll know what you mean) or a viper & star/ brush which will have no problem getting past the lugs that block the flue.