The reason you will hear, "Don't use a synthetic line on a winch" is that 'some' winches have a brake inside the drum. This generates heat when powering out (not free-spool) and when winching in. You have several options:
Get a heat resistant sleeve for the first layer of your winch, very common in the rock crawling community, as almost everyone uses synthetic line now. I have seen synthetic line over heat and fail, so it is a concern.
Get a winch that has an external brake on it instead of one inside the drum (heat source gone)
Most synthetic lines now are a derivative of Spectra-fiber/Dyneema. I believe it was originally created for the shipping industry and now most companies just have a line made for them. Google is your friend.
You should have no trouble at all finding line for your 16,500 pound winch. I have seen synthetic hawse lines the size of a man's bicep. They may not be cheap or plentiful, but getting one for that weight rating is not difficult by any means. Breaking strength on 1/2" rope is 35,500 pounds.