Welcome to the modern Fire and Rescue Service!
Just to put things in perspective, there are a number of FF elements in the Crew and Watch manager role maps, so don't feel too downhearted.
NVQ's are all aquiring the underpinning skills and knowledge and then demonstarting maintenance of skills. It's common place in Industry, such as a fork lift truck driver for example, but frowned upon by us because, well it just is! It's all new and shiny and we never expected it!!
CMMI is an IPDS course .... Personal development. I too have done this course, but have still had to be assessed in job related tests for promotion.
The NVQ programme can be achieved quicker, buit at the cost of quality and possibly not being assessed the correct number of times.
Look at the elemets of the NVQ and see which ones you can provide evidence for ..... and get assessed!
Your other option is to appeal and speak to HR .........
Look on the bright side ........ you are not alone on this one!!