First:
For the benefit of anyone else who wants to tension their wheel, never tension by turning adjacent spokes sequentially around the wheel. When you start with loose spokes you can snug them up to the same number of turns, or by using a nipple driver to the same level relative to the end of the spoke. After that you want to develop the tension around the wheel. I use the 3x3 method which means that you turn the first nippe next to the valve stem, count three spokes (fourth spoke from valve), turn that the same amount, and continue around the wheel untiil you get to the valve stem. For the next round you will start with the second nipple from the valve stem. For the third round you will start with the third nipple from the stem. After three rounds you will have tightened all of the nipples by the same amount, and you will have brought up the tension evenly. I would do it in small increments, like quarter or half turns. You may have to do multiple sets of three rounds before you get up to tension, but it is far better than over stressing the rim.
Second:
If someone brought me a wheel with the backstory you have provided I would start by detensioning the wheel to get it back to a known state. I would inspect carefully any eyelets that were suspect, and in the case of the one shown I might use a rim washer to relieve the stress off of the eyelet. Then I would snug up the spokes with my nipple driver paying attention to any spokes that have a washer since the tension will be off by the thickness of the washer (about a half mm). Once the wheel is even, but loose I would proceed with the 3x3 tensioning until the wheel has tension, but not at final tension. Then I would true it, and follow that with 3x3 up to final tension. After that it shouldn’t need much final truing. Of course there would be stress relieving, and setting nipples, spoke heads, and such. On a job like this there usually isn’t much problem with the set of the spokes since it was already a built wheel.
Good Luck with it.
Jerry