Well, for $1500 dollars I have a couple ideas. First would be to get a second section of the chain harrow to add on behind the first piece. You get MORE drag time with more teeth, so it should work up the sand topping better. You could also get a WIDER piece of pipe, put the two pieces side by side to drag.
I put tires on my chain drag when I need teeth biting down. I have to tie the front of tires on, use two layers across sideways. Maybe one implement tire, because tractor tires for smaller tractors usually don’t weigh enough. Several truck tires do a good job for me, easier to handle than large single tire.
However, getting the weight of drag up for good bite, might be a bit heavy for your dragging machine. Farm sales around here, often have spike drags, adjustable spring tooth drags, maybe 4ft by 6ft, used with the old small tractors. They do have a LOT of drag effect, can make heavy pulling for small machines.
You could advertise wanting one in the paper, Craigslist, see if you get any calls. They are adjustable in depth, but are in the way anytime you are not using them! I kept a piece of old plywood over the top during storage times, in case a loose horse got close and could not step in it. If you do set them very deeply, you can mix your arena footing layers, end up with mud. Should be cheap if you do find one.
We have a leveling device, homemade and donated to the 4-H arena. It is about 8ft wide and 12 or 14ft long, made of heavy 2 or 3 inch round steel bars. The frame has several 8ft cross bars in the center, about 2ft apart. You put a rope or chain on the narrow end, and just drag it around the arena, and it is super at leveling out the surface. Each crossbar is smoothing dirt, with the 12-14ft length preventing drag going up and down in holes or wet places like smaller drags do. So the first couple rounds drag will fill in holes, then just disturb the surface dirt for a cushion effect. Dirt over the bars looks like little snow plows flying along. Never saw anything like it, but it sure does a great job both leveling and smoothing a hard used ring nicely. That arena does speed classes, reining, pleasure, jumping, so some spots are hard used, would need lots of work to get back level if you didn’t have this special drag.
You could have one built at a local welding shop for yourself. Drag does need longer length for staying flat as you drag, spanning low spots and not digging in. The ATV should be able to manage it without problems. Two of us moms easily pulled this drag into place for hitching to a truck, lifted it for moving without a problem. Drag is solid but it wasn’t that heavy.
So a several ideas, should keep you within budget and able to use the ATV.