6 AA cells in series will have a resistance of around 1 Ohm. That means if you take 1 A of current, the voltage will drop from around 9 V to around 8 V. It could be that the resistance wire is taking more than 1 A, and that just supplying the bag sealer from a supply that is better able to supply the current would be a big improvement.
Do you have a multimeter which you could use to measure the voltage when the heater is turned on?
Have you got any spare plug-in power supplies, for instance any old router power supplies? If you have, tell what the ratings are and someone may be able to say if they are worth trying.