So if you look at the table bellow you will see that I am using your calculations to generate the results I need to convert my primary from 120v to 240v using the same core.
That was the whole idea as I have one of those Fluke 8012 multimeters that is 120 and has not voltage switch. I have to rewind the transformer to get it working on 240.
It's too bad you didn't say from the beginning that you are simply rewinding an existing transformer to use 220V that uses 120V as is.
All you have to do is unwind the 120V primary (which you have apparently done) and count the turns. Then you rewind the primary with twice as many turns of wire having 1/2 the cross-sectional area. For example, if the 120V primary is wound with 36 gauge wire (measure it with a micrometer), then you rewind with twice the turns of 39 gauge wire. Wire cross-sectional area halves with an increase of 3 gauge sizes. Wire gauges that are odd numbers, like 39, can be difficult to find.
If the transformer was conservatively designed and doesn't get very hot in use with 120V, you might get away with using a wire gauge 4 times larger--40 gauge in this example.
It appears that Fluke designed the transformer to be usable on 50 Hz as well as 60 Hz, and if you just double the primary turns, that will still be the case. That's probably why they used (apparently) more turns than your calculations say would be necessary.
You don't need to know the permeability of the laminations, or the turns per volt, etc.
Don't try to modify the surface of the laminations by spraying them with clear coat. If you do that, you won't be able to get all the laminations back in place.
Transformer steel laminations come from the factory with an insulating coating. That insulation can be as simple as steam oxide, or better, a coating of magnesium silicate (Carlite):
https://www.totalmateria.com/page.aspx?ID=CheckArticle&site=kts&NM=101Also:
https://www.aksteel.com/sites/default/files/2018-01/carlite201208_1.pdf'If you are careful not to allow the laminations to scrape against one another much when you're disassembling the transformer, the insulating coating, whatever it is, will probably be good enough to just reassemble the laminations without doing anything more to provide an insulating coating. The only effect of a little degradation of the existing coating will be a slight increase in core loss.