Trailers are designed and engineered to be "balanced" for towing when 11-15% of the GVW of the trailer is on the tongue. For a 6,000 lb trailer, as my 210WBS was, that resulted in a tongue weight of just shy of 900 lbs for us (I have a Sherline scale and weighed the tongue several times; 814 lightest, 880 heaviest). Towed beautifully. If you make the tongue lighter, you will find out exactly what "tail wagging" feels like
If you look at the dry weight of your trailer and then multiply that by ~12%, you'll probably find the answer to be ~495 lbs. Start loading the trailer and the gross weight goes up and the tongue weight should also go up. That's why the fresh water tank is usually right over or very close to the axles (a full tank will be "balanced" on the axle), but, the waste tanks will almost always be forward of the axles to keep the weight towards the front. Also why trailers are designed with the bulk of the storage space between the tongue and the axles...keeps the weight on the front. You always want the trailer to be nose heavy, and the heavier the better (for towing), but, always within the design constraints of the hitch and hardware.
A "balanced" trailer is tongue heavy, never neutral (bad) and never, ever, tail heavy...
As for the batteries on the back... If you carry your liquidable assets in the front compartment as gold bricks (heavy, to compensate for moving the batteries), your batteries will not last very long. The bumper area is the roughest riding spot on your trailer and the lead plates contained in your batteries, as they age, get brittle and will disintegrate in short order on rough roads. That's why batteries are put in the front, besides being ballast to keep the tongue heavy; less shock to the casing and better protection against knocks and bashing. We won't go into the mess that all that battery acid will make in the event of a rear end mishap. You would have to reinforce the bumper with gussets down the side frames and would, to be safe, need #6, or heavier, cable to route the current to the front of the trailer in order to pass the current that the battery sometimes needs to provide to the trailer, i.e., a power jack has a 30 amp fuse and can consume close to that under normal use.
If it were me? I'd leave the batteries exactly where they are. The engineers designed the frame and balancing of the trailer for best handling and longevity of the batteries with them protected in the front. If you were going to move them and then compensate for that moved weight, say, installing a 300 lb generator in their place on the tongue, the engineering (bumper reinforcement, cable gauge, routing, etc.) could be worked out, but, just to make the tongue lighter is a bad move...