the tongue weight quote is for an EMPTY trailer. put propane in the tank(s) stuff in the trailer, and a battery or 2 on the tongue and you will be over the 350 lbs. Trailer tongue weight is usually closer to 15% of the trailer weight at a minimum.
As an example our outback trailer had a quoted empty tongue weight which I verified when we bought the trailer of about 750lbs. I figured once the trailer was loaded up and batteries on the tongue and propane in the tanks and the water tank filled I'd be around 1400lbs. I was low. depending on what we have loaded into the trailer tongue weight varies from 1400 to 1550 lbs. near double the true empty weight.
On a 3000 lb LOADED (not empty shipping weight) trailer expect 500lbs on the tongue. One big issue is that trailer mfg design for about 15% tongue weight and vehicle mfg design for a 10% tongue weight. See the problem?
Also if the empty weight of the trailer is 2900lbs, my guess is once you put your stuff in the trailer even with an empty fresh water tank you will be over the 3500lbs.
And the tow rating usually assumes you have NOTHING else loaded into the car, no passengers, no luggage, just you and a full tank of gas.
So, personally I think you will be over the tongue weight and trailer weight by the time your done.
we have friends that pull trailers with an outback, but the trailers they have are much lighter, small "pop up" tent trailers, no frontal area, low overall weight. And it works out well for them.