Ahh, so not cutting a wider slot than design. Eccentric rather than wobbly.
That’s OK, – well par for the course – as many cheap slitting saws only cut (to the maximum depth) on part of the circumference. Look on it as paying the same as a better quality item which uses (and wears) rather more of its teeth than yours. On yours, some teeth will be cutting and possibly some only rubbing (which blunts them quite prematurely). So likely good enough for a single job but not so much longevity, if used regularly and/or often, than a higher quality one.
The wobble saw I used cut a slot from blade kerf to about 10mm wide, depending on how it was set.
Likely need an eccentric arbor, with appropriate run out, so the saw can be turned to accommodate the eccentricity. Don’t think I would bother.