I think you have a problem apart from the type of oil, and it is most likely either a partly blocked screen (as suggested) on the oil pickup or an air leak on the suction of the oil pump (or both), both exacerbated by the relatively heavy oil. But there are other possibilities, including a sticking oil relief valve that is freed by increasing temperature. 
If it was only a problem with high viscosity oil, I would not expect low oil pressure to be a symptom, and particularly not when cold.
John
				
			 
			
		 
			
				
			
			
				John
JDNSW
1986 110 County 3.9 diesel
1970 2a 109 2.25 petrol
			
			
		 
	
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