If you have a high nitrate level then the plants are not enough to keep the ammonia under control, so getting more plants (especially plants with the aerial advantage) is a good idea.
Good to be concerned about the nitrogen cycle bacteria.
By running both filters at the same time, or at least keeping all the media in the tank the bacteria will spread out its population over all the media. Then you can slowly remove the media that will be sold with the can and the remaining media will grow more of the bacteria. Over a period of not less than a month you can get a pretty good population on the new media, and have the can decommissioned for sale.
Another way (faster). Buy a bottle of cycle bacteria that includes Nitrospira species of bacteria. Dose the new filter with this and just do the swap. Remove the can. Give the filter media a quick rinse in water removed from the tank, but keep it in a humid location to keep the bacteria alive. Monitor the tank, and within 24-48 hours if there is more than just a little trace of ammonia then the Nitrospira might be dead. FAST! Put the can back on the tank. If there is just a little ammonia and it goes away then the Nitrospira have taken over and you can go ahead and fully wash out the canister filter media.