I would add a couple of lines so that there is no blurring of intent and eliminate any and all ‘loopholes’:
This law should also apply to any sitting president who seeks reelection. Since this bill has been updated and with stricter rules, any and all evidence of his eligibility previously supplied by the sitting president, will be set aside and he shall be required to resubmit new, in depth, documents asserting his eligbility.
In addition, the chosen running mate of the president shall undergo the same requirements as the president as stated in this bill.
Do you think it would work just to add in the phrase “including incumbents”, which would apply to both Pres candidates and VPres candidates?