I did the same when I first got car. The old oil was very black.Never done it myself but heard that some put in a cheaper oil for a few miles before changing to the preferred oil for the longer term.
The theory is that anyhing loosened after the flushing change is disposed of with the first change. Might put your mind at ease and reduce the flushing oil concentration even further..
I got it hot and drained it, put in some cheap 10w40 semi-synthetic, drove the car for half an hour or so, drained it again, changed the filter and, finally poured in the good stuff.
Now, the oil comes out fairly clean with every oil change.
Oh, and regarding the tappets, if I leave the car standing for a while it tended to be a bit tappety until it warmed up a bit. At the last oil change, I put in some Wynns Hydraulic Valve Treatment and it seems to have helped.
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