You have a "good reason" for a centrefire so apply for one, it's as simple as that.
I don't hold with the myth that you wont be granted a centrefire on first application, it is a rumour and nothing more.
A centrefire and a .22LR would be ideal by the sounds of things.
Mate of mine put in for his fac
He put on it
Fac air rifle
22lr
17hmr
223
Got granted no problem