You can definitely file one joint 1040 return! (The rules actually encourage it, with exceptions you can take advantage of even if you're not officially required to do it that way…)
The IRS starts counting days of presence in the U.S. on the first day of presence during the calendar year in which the taxpayer meets the “substantial presence test.” (That test is discussed here. Also see example 4 here, of a J1 Visa holder with slightly different circumstances, but still relevant.)
In your wife’s case, the five J1 years were the maximum before meeting the test anyway, so she would have satisfied it even without becoming a H1B. But more importantly (and what you were really concerned about), the earlier days from that year of meeting the test when the taxpayer was an “exempt individual” are no longer considered “exempt” for the purposes of the test. So she’s now a U.S. resident for tax purposes for all of 2022, and required to file accordingly (either jointly with you or separately, but no more 1040NR).
I hope that helps. Thanks Budi1782!
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