First thing is to confirm the condition of the belts . You comment that you may consider doing the work yourself so I guess you would be quite happy removing the covers on the 3 cambelts to check
( there are 3 belts , one big one on the front and a small one on the rear of each head )
If you find a snapped belt , then you know where you are ! There is also the possibility of a slipped belt that has jumped a couple of teeth due to lack of tension , and may cause similar damage such as bent valves
If you were to do this repair yourself then the complex bit is refitting and timing the new belts . Removing the heads themselves holds no particular challenges .
I have done this to replace worn valve stem oil seals , and the one down side was that there are 24 valves to handle , if you go as far as removing the valves !
Not a quick job at all , but very doable if you are competent , and even enjoyable if you like tinkering
On the other hand , before leaving it with a garage I would want to be very reassured of their experience and knowledge .