Married Filing Separately on W4 with a total of 3 jobs between couple

My wife and I got married in June and I have been super confused about how to handle our respective W4 forms. We just started these jobs about a month or so ago and we want to make sure our information is correct.

My wife works a full-time salary position (a little over $59,000 a year) and I work two part-time positions at 20 hours each per week (40 hours total between the two) and get paid basically the same at each job ($22 an hour vs. $20 an hour). We were attempting to update our W4 info as Married Filing Jointly, however, due to the nature of this year (we both graduated college and had a few odd jobs earlier in the year with varying hours totaling 7 different jobs between us), it has been a headache and a half trying to incorporate all the info into the IRS calculator correctly and I really don't want to under withhold taxes.

Is the following strategy viable?

My wife indicates Married Filing Separately on her W4 and leaves the rest of the sheet blank (we don't have kids, we both work W2 jobs, no deductions, etc.).

I also indicate Married Filing Separately on my W4s and check Step 2C on both forms indicating that I have two jobs of similar pay scale (~$22,000 a year for one and ~$20,000 the other).

Will this strategy result in enough withholdings and avoid paying any remaining taxes this coming tax season? Or do my two jobs complicate this? We plan on actually filing our taxes as Married Filing Jointly when it comes to the return, we just want to ensure we are withholding enough according to our W4 until then. I understand we also may be withholding more than we need to with this strategy but I'm simply prioritizing withholding enough as opposed to maximizing returns and interest and what not.