EOQ and Average Level

And if you equate them, they give EOQ =maximum level - minimum level, even daunting.

If there is no buffer/safety stock, then the average level is half of the order quantity (which is true whatever quantity that they order each time, whether or not the choose to order the economic order quantity. This is because the minimum level is 0 and the maximum level is the order quantity (as I explain in my free lectures). If they carry buffer/safety stock, then both the minimum and maximum levels will be higher by the amount of the buffer/safety stock, and so the average level will be higher by the amount of the buffer/safety stock as well (and again, I explain this in my lectures). Equating them would be meaningless, but it means that the order quantity (whether or not they order the EOQ) must be equal to the maximum level minus the minimum level. But there is nothing daunting about this at all. If there is buffer/safety stock then this would be the level immediately before a new order arrives - i.e. the minimum level. As soon as a new order arrives, the level go up by the amount of the order. So the maximum level has to be the minimum level plus the amount of the order.

My surprise is that the two formulas never agree when I test them both

If that is the case then you are not applying it correctly. However appreciate that this is not a maths exam and so do not simply learn formula.