You need to be at or below 350 on the tongue, not just closer to it. 

Be careful moving weight rearwards to get the tongue weight down, that will increase sway risk. Don't let the tongue weight get below 10% of the trailer weight as an absolute minimum, preferably 11-12%, and consider that this minimum applies to all expected loading conditions, not just the load out at the beginning of a trip. Don't depend on the Hayes antisway system to save you, you need to start with a stable rig and consider the Hayes system as a backup. 

If you think these tight constraints are kinda like being stuck in a little box with no room to maneuver you are absolutely right. This is the kind of thing that makes folks get a higher capacity tow vehicle. Please be careful and stay safe.

I think you will be okay with the Hayes. Please check with Hayes to make sure it is one that is newer or if older has had the recall applied to it. See this for details. If you had purchased direct from Hayes, it would not be an issue, but I have no idea how old the unit you purchased is since you say you purchased it on ebay.

Just a note that the Chesapeake Bay Bridge (which is in Maryland) and the Chesapeake Bay Bridge Tunnel (which in is Virginia) are two different things.

But yes, at the CBBT, you just let the toll taker that your propane is turned off.

At the HRBT, you have to pull into the inspection station and tell them that your propane is turned off. They write down your license plate number on their log.

I hate motels.

I am very familiar with the bridges as I used to commute across the HRBT.  We are going to the Eastern shore next week so I will keep a check on conditions before leaving. I thiink on the Chesapeake Bay bridge you don't pull off you just tell the toll person the propane is shut off.  We are going to Cape Charles so it is only about an hour or so trip.

When you say 50 lbs on the trailer do you mean the trailer weighed in at 3450 lbs? And 100 total means the combined rig weighed in at 100 lbs under the MCGVWR on your driver's door sticker? Don't forget passengers, fuel, and your weight distribution hitch in your calculations. 

As far as fuel economy is concerned you would get pretty much the same fuel burn with a heavier tow vehicle under the same conditions. We all do. Those that report worse fuel economy are driving faster, hitting a headwind, or are climbing hills or mountains. I drive at 60 and get 14 mpg on flat ground with no wind. I would get about 15.5 at 55. 

Why? Because air drag on the trailer is the dominant hp demand when towing on flat ground. That drag doesn't change with the size of your TV, because the trailer frontal area is always larger than the tow vehicle's,  but it goes up really fast with speed (its proportional to the square of the air speed). Most all modern engines have similar efficiency, they have to or that manufacturer would go out of business. So the only thing that really changes with a heavier TV is rolling resistance (which is proportional to total rig weight) but that is a small effect. 

You will feel like the towing is going fine....until its not. That will be in bad weather or in the mountains or when you have to make a sudden lane change.  I know I64 in the Norfolk area very well. I used to live on the Outer Banks. You get to go over one of the few bridges in the country where you have to stop and prove your propane tank is shut off. Those bridges can get really scary when there is a blow creating a cross wind, its best to stay off them towing when there is a nor'easter or tropical storm. 

Sometimes I think folks acquire an RV because it will be a cheap way to travel.  I have found that it is not necessarily cheaper than traveling by car and staying in a hotel or motel.  In fact I have stayed in a motel with my RPod parked in the motel lot when I was trying to cover a lot of miles and didn't want to take time to set up and take down the trailer.  There are many cost in addition to the purchase of your RV.  As was discussed here many of us have had to upgrade our everyday ride to comfortably tow my Pod.  There is the additional cost for fuel, additional time on the road to tow at a lower speed, additional cost for campsites, additional time to setup and take down and then all the specialized stuff we buy for our camper.

That said, I have "camped" or "RVed" for many years.  I like being out in nature.  I like being able to be right by the natural attraction in a state or national campground.  I like being in my own bed, with my own sheets and pillows, a shower only my family uses, and a mattress that I've selected to suit me.  I like getting up on the morning with my dog going for a walk and visiting with other RVers all while dressed in my pajamas and no one thinking a thing about it.  How often do you visit with your neighbors while staying in a hotel or motel?  I'd like to think I'm saving money, but as an old accountant I know I'm not and I don't care.  I've drank the koolaid, I'm in it for the lifestyle.  

+1. And the only way to really know that is to load up and get an actual weight at a public scale.