I don't know if this will work with your pattern since I can't see it, but it is possible in some cases to knit intarsia in the round.
The first round, as you found out, is not problem, but now your yarn is in the wrong place, right?
Since it is only one stitch from what I see, just turn the work around and purl the contrasting color. The main color can be stranded across the back.
It's hard for me to picture this for only one stitch, let me know if this works.
"Trust the pattern!"
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IngridKH on Ravelry