All credit for this solution must go to the Embedded Artists' support team, whom I contacted for help with this.
Firstly, change your MCUXpresso project's pre-processor symbols: XIP_HEADER_ENABLE must be set to 0. If you have a multi-core project, you must change this for the master project (the slave project should already be like this). Build your project to generate the updated build output file (.axf).
Secondly, make sure your stack location settings are like the default:

The issue I had with the .bin file being too large was because I changed my stack location to "Start". The default is "End".
When using the MCUXpresso Secure Provisioning Tool, in the write tab, select the build output file (.axf) for the "Source Executable Image". The "Start address" will be automatically populated. Next, change "DCD (binary)" to "Custom" and navigate to your target's SDRAM_dcd.bin file, included in the Provisioning Tool's directory. For me, the GUI looks like this:

Now you can click on "Build Image", and it will work. Then go to the "Write image" tab, select the build image that you want to use (_nopadding.bin file), click "Start FlashLoader" and then "Write Image".