Hi,
No OPPO has EVER "clicked"
My guess is you are hearing the sound of the relays in your AVR or Pre/Pro as they reacquire the HDMI audio bitstream.
IME it mainly occurs at the start of a movie when several promo trailers are shown and the movies Main Menu appears.
I believe the AVR or Pre/Pro has to lock on to the HDMI audio bitstream and it breaks as each new trailer kicks in.
Hearing this is common and actually a sign of high quality equipment.
But once the movie begins it should stop!!!
If, after close inspection, you still believe the clicking IS coming from the OPPO then I would definitely contact Customer Service!!!
On a side note the OPPO 105 IS a decent step up from your 83SE and offers higher quality audio with EXTRA attention paid to analog stereo output and way more cool features.
It's the EXACT upgrade path I took and I LOVE it.
Lastly, as you are using a Projector(?) you may benefit more with the 105D as the "D" indicates Darbee Video on board.
Darbee is a video enhancement tool that should make a MORE noticeable difference in PQ as the screen size increases.
Cheers