The problem you desribe is most likely "block porosity". Moss motors sells an 'oilway relair kit' that, as I understand it, was originally developed by Southern Carburetor. What they determined is that some oilways are very close to water jackets and as these motors get older and some rust/scale comes off the water jackets the natural porosity of the cast iron allows oil to seep into the water passages - oil at 40+psi vs water at 7psi = oil wins. One way of confirming is to see if you have any water in the oil, this will usually be the case with a bad gasket or crack but if it's the block porosity then it is a one way deal and you should have no water in the oil, just oil in the water.
I had this happen to a motor of mine about 6-8 years ago and I had a machine shop install an oilway repair kit. This consists of drilling out the oil galleries a bit and inserting stainless steel tubes along with a sealant. Tremendous amount of work because it requires stripping the motor down to a bare block for the machining and cleaning. Sounds good in theory but in my case it had no effect and I eventually scrapped the block.
For the last 3 years I have been dealing with it again in another block and I am unwilling to try the oilway repair again - it is very dependant on quality machining and trusting the sealant to seal. What I have found in my case is that I can go 500 miles or more without a problem and then I drain and flush with detergent a couple of times and am good to go. Cooling has not been a problem because oil will transfer heat almost as well as water. The one plus is you don't need water pump lube. Other than the mess and hassle of flushing the system, I can tell you that I have driven around 10k miles with my current motor and it runs fine. I also should note that I vintage race mine and therfore don't run antifreeze so I don't have the environmental issues of dealing with contaminated antifreeze
My suggestion is to find another block and build another motor. However, the one problem with this is I haven't found a good way to pressure test a block prior to machining and assembling so you may end up with the same problem. Pressure testing is difficult because this is a very slow seepage not an open crack.
The DMD Australia website has some pictures of a sawn open block and head and you can see how close the passages are to each other. SC Parts also has soome info in this I think, as well as Moss Motors.
Good luck
Dave Phillips