I may have answered part of this after you. Read my post above.
Yes, I'm guessing it quit knocking after the oil got circulated. I don't know, you could be right. I would just hate to spend the time and money to replace the heads the right way then have a bearing go out or something.
I would ensure your bottom end is toast before dropping the coin for a complete reman. My 04 was making what sounded like a bottom end clatter, but I thought it was more like lifter noise, either from a collapsed lifter or one that was stuck from the water in the oil. The way you describe your "bottom end" noise and when it goes away, etc is exactly what I experienced. I had multiple life long motorheads listen to mine, and there was consensus that it was lifters and not rods, etc. The knock of a bottom end is a distinct thump vs. lifter chatter. What I have noticed recently is when I had the oil changed, the lifter noise is completely gone, at least for the short term. I know as the oil gets fouled by water, it will most likely return. I would suspect if you have fresh(er) oil in there, that is why it quieted down. With new oil, I saw a boost in oil pressure readings. I am still debating between a take out engine and just doing heads. I know driving it as is can cause further damage, but with 276k on it, I think I've got my money's worth and it does drive and sound normal, even though I know there is likely a head crack dribbling water in and fouling the oil and oil system. If yours is not too far gone, you may be able to correct with just heads. Do you really want to drop $3k+ into an old truck that is not worth much more than $3k? If the repair cost is not important and you're keeping it forever, then that changes things dramatically.
My oil sample came back high in water, sodium, potassium, and unfortunately lead. Lead = bearings from what I know. It will be interesting to see what yours come back with.
It sucks this happening to what otherwise is a good engine, the LS family, but I will say that I am impressed with how it's holding up, even with the water in the oil. I know I better be careful to not jinx myself now.
I am sorta looking for one of the L33's that someone previously mentioned. In Socal where I am, there are A LOT of wrecking yards, self serve pick a part, and full serve pick a parts, so there are plentiful replacement options in my area. I know I am gambling with permanent damage to my existing L59, but I'm waiting for the right option to come along to repair mine or swap out complete. An engine swap doesn't scare me. BTDT in my 69 Bronco installed a 94 Ford Lightning 351W. With this being a direct replacement, it's just unbolt and bolt in.