Here's a company that makes a good selection, you could even get one with no rails. Click on single or double axle and you can do a dealer search.

Big Tex Trailers | Utility | Auto | Dump | Equipment Trailer

 

A buddy of mine had a very similar situation to what you have! Heavy enough trailer, but needed more area for 2 atv's! He did 2 stages!

1st stage: was good enough, but only temporary. He go some good heavy 2x4's and laid them across the front of the trailer and they were cut to length for the smaller atv. He then drilled holes through the boards and angle iron on the trailer and bolted them together. He used some of the drop off of the boards to put in the middle for support! They did that for about 6 months! It worked good and solid, was cheap, but doesn't have the greatest appearance, and they couldn't use the ramps that came with the trailer. With this set up there was one atv on the front of the trailer sideways and one towards the back of the trailer loaded normal.

2nd stage: they cut the rails off from the trailer tire forward. And reinstalled them at a 45 degree angle on one side. The other side they made the railing detachable as well as on an angle. Thus making it easer to load, and not look as thrown together as the other way. How ever it will require welding and some extra angle iron.

 

you could easily mod that trailer so it was safe secure and strong. Get some square tube as long as your sides and front. Cut off your sides. Take the square tube and lay it down where the sides used to be on the deck. Make sure your trailer is level and not twisted by putting jack stands front and back. Weld the tube about every 6" with about a 1" weld alternating where the welds are on the inside and outside. Then you can put some pockets on the outside and then you can slide your sides back in.