Jason, I have determined my 630 was a 1960 also by the casting numbers on the rear wheels and engine block. I also had no side panels when I got it. I have them now but the palte is gone and obviously I have no idea what the serial number is. Just for grinns what is the engine serial nunber stamped on the right side of the block behind the throttle linkage.
Mine is 313 S03006, block casting date is 12/27/1960 and wheel castings are in 12/XX/59. This should make it a very early model 630 and it too has the pan seat which I think was pretty early as most 630s I have seen photos of have the delux padded seats.
If we can find someone on this forum that still has the serial number plate on another 1960 model with our engine numbers we might get close to a proper serial number range. Rich Tworek says the only way to get a serial number using the engine number is to get someone to go through each of the build cards and compare, quite expensive if Case does it.