as you have stated above . some forces did let you remove them from FAC but i think most that did no longer let you . you could say its sentimental reasons and see what they say ,you may get lucky.
what rifle is it?
some rifles have the serial number only on the barrels if a break barrel rifle so it MAY be possible to detune and change the barrel. possibly hand the FAC barrel in ?
and if PCP you may be able to change the block as in a theoben rapid and hand in the FAC rated one .
only your firearm office will be able to confirm this.