Yeah, you have sort of a mess there but not terrible, yet anyway. I'd certainly get the radiator repaired if the shop can do it. Probably can. If you end up having to replace the radiator, do some searching on Amazon . Also eBay, etc. For example on Amazon I do not find an immediate replacement for the MF 1250. The companies (for ex. Kumar Bros USA) selling on Amazon for old Fords etc. may very well sell them for your MF 1250 and could be contacted to ask via a Google search on the company name. Another source might be a tractor salvage yard (suggest call Wengers of Myerstown PA and see if they have one OR can give a lead on where to find one. They are VERY good and usually helpful.)
In your travels hunting stuff beware that there was another MF 1250 which was a huge machine (bends in the middle) and NOT a compact so don't get off on a wrong path there.
There are some larger questions. 1) Why was the coolant rising and coming up out of the radiator when the motor ran? That MIGHT be a totally plugged radiator not letting fluid through it. OR it might be compression getting into the coolant from a blown head gasket or even a cracked head or block. One thing at a time -- let's not assume a disaster yet. 2) What was causing the engine not to turn over? Was the battery OK? Could be water lock or some other issue. Until you get a good radiator back on it you cannot run a pressure test to look for blown head gaskets or worse ... so... as EGON said, do a compression test on the cylinders and that can be done in parallel with the radiator chasing. If it needs a head gasket there is no way around that...
How much of this stuff can you do yourself? Competently I must ask? If you are leery of tackling replacing the radiator and running compression tests yourself, I suggest this sequence
1) resolve the radiator issue getting it repaired for $60 or finding a replacement.
2) Find a general tractor repair shop. Even a truck/car general repair shop. Get them to do whatever you are not comfortable doing.
You have the $1000 refund to put towards the work. You MIGHT luck out and not have to put a whole lot more into it.
Did the dealer who sold it to you have any info at all on the trrecord.