I met an A330/340 FO recently who only had 7,000 hours when hired - mostly A320 and all FO time. Despite what people say about that fleet, he is quite happy. True he will sit on those airplanes for awhile before joining the A380, but he is enjoying the newer A340 destinations (for him since he primarily flew A330) and checking-off the variety of destinations and layovers. He enjoys his fleets and the flying - others may not as much for reasons already discussed.
You never know, with your 767 time, maybe you will get assigned the 777. You could stress your Boeing time and always request the 777 if you really want it - although that might fall on deaf ears depending upon staffing needs at the time. Look at it from a training risk perspective. Doesn't hurt to ask for it if you get hired (but that might not work in the end).
Qatar is also hiring quite a bit. Depending upon your timing, your 767 experience could qualify you for the 787 as that fleet starts to ramp-up. The 777 fleet is also a good possibility given your widebody Boeing experience.
Good luck!