I finally received a reply from the FAA on the original question. It is very thorough and hopefully can help somebody else with the same question down the road.
Question: Can a subpart H flight instructor certificate issued in accordance with Title 14 Code of Federal Regulations (14 CFR) part 61 be reinstated by completing a part 61 subpart K flight instructor sport pilot practical test with sport pilot rating, for a category and class not held by the instructor?
Answer: No, a practical test for a 14 CFR part 61 subpart K flight instructor sport pilot rating (for a new category and class not held on that expired subpart H flight instructor certificate) cannot be used to reinstate that expired part 61 subpart H flight instructor certificate.
Basis: You cannot add a subpart K flight instructor “sport pilot rating” to a current or expired subpart H flight instructor certificate. You can only add a sport pilot “privilege” to a subpart H flight instructor certificate that has not expired.
To add a powered parachute category and class privilege to an existing flight instructor certificate, per 14 CFR § 61.419(b), How do I obtain privileges to provide training in an additional category or class of light-sport aircraft?, the applicant must complete training, receive an instructor endorsement and successfully complete a subsequent proficiency check. However, the subpart H flight instructor certificate must not be expired in order to add a new sport pilot category and class “privilege” to that instructor certificate.
The FAA notes that a proficiency check is not equivalent to a practical test and does not qualify for the reinstatement of a part 61 subpart H flight instructor certificate based on § 61.199, Reinstatement requirements of an expired flight instructor certificate, and specifically § 61.199(a)(2), completion of a “flight instructor certification practical test for an additional rating.”
The FAA does not issue multiple flight instructor certificates to one person. The successful completion of a practical test for a flight instructor certificate with a sport pilot rating would result with the issuance of a subpart K flight instructor certificate. However, a person who possesses an expired flight instructor certificate would need to surrender that expired flight instructor certificate before the FAA would issue a subpart K flight instructor certificate with a sport pilot rating to that same person.
The FAA recognizes that pilots with a higher grade of pilot or flight instructor certificate can exercise the privileges of a lower grade of certificate. With that understanding and a review of § 61.427, What must I do if my flight instructor certificate with a sport pilot rating expires?, and § 61.199, Reinstatement requirements of an expired flight instructor certificate, the FAA also recognizes that an applicant can reinstate their Subpart H flight instructor certificate by accomplishing a “practical test” with a sport pilot examiner conducted in a light sport aircraft. However, the flight instructor reinstatement practical test must be accomplished in the same category and class of aircraft for a rating already listed on the flight instructor’s expired certificate.
Because you do not hold a powered parachute rating on your expired subpart H flight instructor certificate, you do not qualify for reinstatement under § 61.427. Reinstatement allowances under §61.199 only apply if conducting a flight instructor practical test for other than a “sport pilot rating” because a flight instructor practical test for a sport pilot rating will result in the issuance of a subpart K flight instructor certificate.
In summary, the information you received is correct. The only method to add a new category and class sport pilot “privilege” to an existing flight instructor certificate is by completing a proficiency check described in § 61.419, and that flight instructor certificate must not be expired.
You would need to reinstate your subpart H flight instructor certificate in order to add a new sport pilot category and class “privilege” to that instructor certificate, or surrender your expired subpart H flight instructor certificate and then complete a flight instructor practical test to obtain the new subpart K flight instructor certificate with a sport pilot rating.