Backfires are always a lean condition. This can come from bad timing or a stretched timing chain- 351Cs are extremely hard on cam chains. I've seen them unusable at 25,000 miles. Lean can also come from an air leak- like a bad intake gasket. The 351C has a waterless intake so a leak will only be air (or oil from the lifter galley) and you won't see it. You likely do not have a bad cam; more likely is rusty rings/cylinder bores and a bad intake gasket. The oil burning may get better with more running if its the rings. Do you have an EGR vave? The aluminum plate adapter under the carb is notorious for burning thru, then sucking air. FYI, there is a std way of running a compression check: first, disconnect any electronic ignition from DC power, then remove all 8 plugs. Second, block the throttle wide open. third, crank the engine at least 3 turns to guarantee a compression stroke. A healthy Cleveland, done this way, should show around 140psi. Now, repeat with a teaspoon of oil. An increase in pressure of about 25psi indicates unsealed rings. If low and oil doesn't help, indicates unsealed valves. Much more valuable than a compression test is a leakdown test- it'll tell you how bad, and where, and what. Good luck-
