From looking through the Case parts search pages for parts commonality I believe the engine/gear train on the Round nose and the 300 square front utility are basically the same and the loader will probably fit. There is a fellow on this forum that is trying to sell his 311 with a loader on it, you may send him an e-mail or reply to his post and he can tell you what is on his tractor.
The eagle hitch was introduced by J. I. Case in 1949 I think on the VAC and followed in 1952 on the DC and SC. This 3pt system was the Case version of the Fergusion 3pt and was radically different enough to get around the patent I believe. They kept it until 1964. The draft arms on the eagle hitch are ridgid and your tools don't flop around like they do on the conventional Ferguson type 3 pt. Instead of the ball joint ends on the draft arms to connect to the implement and having to get off and push and shove around on the implement to line it up, slip the pins through the ball joint and put your clik pins in to hold the arms on, the Case system had an eagle claw looking device hat you opened up before getting on the tractor. Or if you left the little ropes or chains attached to the hitch lock latches you could just pull the latches up to disengage, back up to the implement with the hitch lock tabs contacing the implement's lift pins, open the eagle hitch, lift the arms up and pull forward to auto latch. No getting on or off the tractor. To unhook, the same thing was done, pull the latch cord up to disengage, set the implement down, back up to disengage the locks and drop the draft arms. Theoretically you could hook up to your plow or what ever, plow up the garden, unhook the plow and hook up to the disk and till it up, unhook the disk and put the tractor in the shed without ever leaving the seat.
The system was nearly this good. Usually the unlatch cords/chains never stayed on and the unlock tabs were generally broken off the lock links, but basically without a lot of on and off one person could hook up or drop the tool by themselves. I used this system from the time I was about 8 years old until I left home when I was 21 and some afterwards on visits and I loved the system. My current 630 has the eagle hitch!!
Some will argue, but I think the eagle hitch is far superior to any competing hitch on the market then or now. If you don't believe its a good system, cruise around in ebay and you will see a quick hook up conversion system for your conventional 3 pt arms that looks very similar to the eagle hitch claws. If it was so bad why is somebody still making money with the idea? BTW Tenneco had purchsed Case by the time the eagle hitch was discontinued. Don't know if it was a corp. philosophical change from the old Case designers or just new blood trying to make their mark.