First off it would be good to know if your
L3400 is gear or hydro. You'll need to go by the PTO power too. I just looked and if your tractor is hydostatic drive you have 28.5 pto horsepower. I tried to find the width of your rear tires and it would appear to be around 52 inches. If your wanting a really nice tiller look at the Befco T50 series. Look at the one that is 58 inches wide and rated for 25 horsepower. It has lots of features.
Tills extra deep at 8 3/8 inches. Catagory 4 pto shaft. 100 wt chain drive. Just has lots of little extras on it even has a side shift if you ever get a bigger tractor. That would help you take out one tire which is fine really. Good weight for your tractor also. We've used its economy model, Rotomec, here for years with no issues at all. The T40 series would be good if your watching you dimes. Just about any tiller 60 inches or under will serve you well. I don't know of any "lemon" brands frankly. Tillers are pretty simple and about the only think you need to watch for is to make sure your slip clutch is funtional every spring. If your not going to do that better get a sear bolt protected PTO shaft.
BEFCO - Products - Rotary tillers - Till-rite T50 They are in Stoney Point NC.
A tiller is perfect for what your wanting to do. I leave mine on for ballast when I'm using my loader. There is no need to ever sharpen your blades. I like the standard front rotation as it does a better job in my opinion of tilling under green stuff for "green manures". My two tillers are chain drive and never had any trouble at all. Some say gear drive is better. I think they might be right to some extent but lots of heavy duty chain tillers out there working hard year after year. Most tillers will till slightly wider than they are listed by about two inches. Just the way the soil breaks up. Befco is made in Italy same as most tillers. Sicma and Maschio are other top quality Italian tillers that are sold under names like John Deere, Rhino, Bushhog and a host of other names. Look at them all but look close at the Befco tillers.