If you don't have time to undertake your continuous improvement projects then why not consider this approach?
If you spend your whole day running around putting out fires then you will probably find that you just don't get time to undertake your continuous improvement project work.
I've been there and I'm sure many of you reading this will feel the same.
If you break down your project tasks into small chunks (let's say chunks that are 5 to 15 minutes in duration) then you can legitimately complete these tasks at the start of the working day.
The fires will still be waiting for you, but over time they will lessen. Hopefully after a couple of weeks of using this approach you will start to make some time elsewhere in your diary to really get your teeth into continuous improvement.
Flipping your priorities, for even a short period, may be a really powerful strategy for you to use.
P.S. If you are looking for a simple strategy to generate your continuous improvement ideas then why not try my book 'Effective Continuous Improvement'?