Even if you do have to pack your tool up rather than a whole stack of thin packing use a mix of sizes so you reduce the total number eg replace 3 or 4 of those hack saw blades with a bit of 1/8" or 3mm flat bar.
The fact the knurled adjusting wheel on your tool holder is down to it's max suggests the tool post is too small or as John says needs packing up.
This pic shows how the angle of tilt gets less as the bar diameter and therefor minimum hole size increases
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And this some of the square holders with bars, you could drill the hole offset to thetop which would also put the bar higher in the tool holder.
![20210725_150641[1].jpg 20210725_150641[1].jpg](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)