RE: My plane experiences snaking
Balance tabs are restricted in their percentage to avoid the issue being discussed but there are two other issues that factor. 1. The lever arm of the balance tab. The longer fore-n-aft the balance tab is the greater its lever and thus likely the percentage rule more conservative. 2. Any unusual air flow. For example if the airflow favors that upper fin area and the balance tab area over the broader area of the rudder then again the balance tab area should be conservative.
If the balance tab is over sized or leveraged, it will produce over controlling that will take advantage of the slightest bit of play in control linkages to produce hard impacting rudder shifts. In fact there is some danger here because if an unsecured metal clevis is in the system, the oscillations will greatly accelerate thread wear and within a few flights failure could occur. So, if the plan is to fly it this way, keep a check that clevises are locked by a back up nut.
I know you don't want to do surgery... but it seems to me that it is warranted. I'd not do away with the balance tab by cutting it off and adding it to the stab (major surgery), but I'd cut a little off the top to reduce the tab percentage (minor surgery).