Simply END the signature requirement altogether. There is no ■■■■■■■ need for it.
Simply impose a qualifying fee high enough to discourage nuisance candidates. Perhaps $5,000 to $10,000 for Federal and Statewide Offices and Judicial Offices, somewhat less for county and municipal offices. Perhaps make some or all of that refundable if a candidate crosses a certain vote threshold, as is the case in the United Kingdom.
And as the article points out, gathering signatures has become an industry rife with fraud and abuse and at a prevailing rate of $4.00 a signature in some places, it is just INVITING signature collectors to invent fraudulent signatures.
Just abolish signature collection and establish a filing fee instead.
It does not take very long to verify a petition signture - perhaps 15 to 30 seconds, per signature.
Speaking as someone who has spent more hours than you can possibly imagine doing exactly that.
New York has an interesting spin on petitioning, as well - there’s a signature requirement, but collected signatures are public, and opposing candidates can challenge signatures individually. This results in all candidates verifying their opponent’s signatures.