uh oh..... set back. water in oil

Was the smoke out of both banks of the exhaust or just one? (Assuming you have dual exhausts) That is a lot of coolant that went in the oil so something let go for sure; not just a seep IMHO.

As for your flushing.....sounds like you're doing a good job. I am doing a similar thing on an Opel engine that got some coolant into it. What we did:
Poured alcohol (then diesel later) in the heads to clean them out. Flushed and ran the oil pump while slowly rotating the engine 2x by hand to get the passages as clean as possible like you are doing; did this for 1 91% alcohol flush (to absorb some of the water) and then 4 separate diesel flushes. The key is the change the flushing agent a lot IMHO, and diesel is a modest lubricant; it cam out cleaner each time. Then added that same cheapo Walmart SN oil with half a bottle of Rislone Oil Treatment to push up the ZDDP levels to around 1500 ppm (where you want it to be) and pumped it around the same way while turning the crank by hand. 10 minutes running with that 1st oil and changed the oil; that 1st change was really dirty and thin from getting out the diesel, but very little coolant was left in the engine by that point; it was mostly gunk from the used engine being cleansed with diesel. Waiting for the 2nd oil batch to come out after a few heat cycles, but it still looks clean after the first 5 minutes of running.

And when you get that 1st and 2nd oil changes out, wait overnight before you drain and let the first qt come out of the drain slowly so you can observe any separated water or coolant. Then let it set in a pan and put the last qt the bottom of the pan in a glass jar to let it separate for a couple of days; you will get some idea of how much coolant you are still getting out. (How well it separates depends on the oil....)

In your case, I'd pull all the lifters and tap them out is disassemble them. And take the rocker shafts off and flush them; they get very little oil in the priming process unless you park the crank at the right angles for a while, so your flushing will not likely clean the rocker system well.

Even with the intake gasket realization, I'd still pull the timing cover and investigate that.

Hope you get it!