The idea that the traditional method of Hadith criticism can be reconciled with the historical critical method (HCM) is unrealistic. Some minor overlaps aside, the 2 methods have completely different premises.

Bluntly: The traditional method assumes God wouldn't leave his people without guidance & so he clandestinely oversaw the transmission process of Hadith throughout history making sure a "true" kernel survives that can be separated from the "false" material using the right logic

But the HCM is open to the possibility that certain data about the Prophet's life & teachings cannot be recovered from the Hadith corpus, as it has been shaped by later generations who suppressed certain data or even invented parts of it wholesale.

Moreover even if the HCM happened to verify a traditionally "sound" isnad that goes all the way to a "trustworthy" Companion citing the Prophet (i.e., that an isnad accurately describes a hadith's transmission) that still wouldn't confirm the traditional method. Because...

...The HCM assumes that Companions may have lied or transmitted things inaccurately. In other words, the isnad may contain clues about who transmitted a hadith but it doesn't tell us if the earliest confirmable transmitter told the truth.

& let's assume that the hadith innama l-a'mal bi-l-niyyat was subjected to an objective Hadith analysis by a competent scholar whom you trust & it was discovered that this hadith is a late invention. Then what? Would Muslims reject this hadith foundational to their belief system?

Most Muslims probably wouldn't reject it. The traditional science of Hadith in most cases isn't really concerned with uncovering the earliest traceable origins of hadiths but with defending the integrity of an existing corpus of "sound" Hadith.

In closing: yes there's much to admire in the traditional method of Hadith analysis but its utility for the historian is very limited. There's more to say but I will leave things here.