The OP doesn't state what his original cartridge is.... if he has a newer AT-LP120 then it should be an AT-95E with under normal circumstances has plenty of clearance between it, and the record surface, if balanced correctly.... - he makes a point of mentioning a lack of clearance.... so unless he has replaced the original slipmat with a very 'tall' rubber mat, and not adjusted the VTA control beneath the arm, or is tracking the original cartridge at far too high-a VTF, then there shouldn't be a problem there!
In fact, Having used Ortofon before, they leave very little clearance below the cartridge and record anyway - the AT-95 if set correctly should leave a couple of millimetres at very least - if tracking at around 2 grams...

With my AT-LP120USB-HC, which has the newer 10gram headshell design, I added, using a strong "No More Nails" double sided tape (cut into very small squares) 4x 3gram steel washers to the back of the stock counterweight, so that it now is far more forward towards the bearing, when balancing the arm and setting VTF - gives more stability, and less resonance....
And as a happy byproduct of this, when the AT-95E cartridge is balanced and tracking nicely at 2.2grams, if I remove this cart/headshel, and replace with an old Shure M75-6 cartridge body (no plastic housing, only the metal clip) which is fitted onto a heavier, solid piece headshell, with a fine wire strapped around both L & R + posts, and using an N78 stylus, it tracks at around 3 grams weight, and plays 78's perfectly well

I don't have to adjust tracking or rebalance - it just falls nicely into that tracking force - checked with digital scales

Putting the AT95E/headshell back, then becomes the original 2.2 grams.... I think the 'solid' headshell/Shure, is just that-much heavier

And of course, neither cartridge is riding too 'low' or close to the record surface....