I have found that R/T fluency goes hand in hand with flying currency. The more you do, the less you have to think about it.
It is very easy to achieve brain overload when flying, particularly when converting to a new type, venturing into unfamiliar airspace, or dealing with unforeseen problems - and the first thing to go out of the window is usually the radio work!
I am by no means an oracle on this subject, but have a CPL/IR and regularly fly jets at relatively low-level around England and Wales and have adopted the following approach to R/T:
1. Know who you are going to talk to before you set out and have the frequencies written down in the order in which you expect to use them.
2. Always have the next expected frequency set on standby.
3. Use LARS as much as possible and ask for a radar information service - you will usually be passed from one agency to the next without having to re-introduce yourself every time you change frequencies.
4. Think about what the guy/gal on the ground needs to know in order to help you - Who are you? What are you? Where are you (and how high)? Where are you going? and What do you want from them?
Preparation really is the key, particularly when you are travelling fast, and will free up your brain capacity for the most important job of all - flying the aeroplane!