Allow me to begin with a bit of a red herring before coming to partial answers.
It would be natural to assume that the case of gilded/gilt is parallel to the case of burned/burnt. In the latter case, these phenomena play together:
- The inclination to regularise verb forms.
- The reluctance to change the spelling of adjectives.
- The fact that in this case the US is more progressive than the UK.
The result is as follows, according to data from the Google Ngram Viewer:
- BE has only a slight preference for burned when used unambiguously as a verb form, and at the beginning of the century there was actually still a slight preference for burnt even in this context. For attributive use, burnt is still twice as common as burned in BE.
- AE prefers burned for clear verb form use since the middle of the 19th century. Since the early 20th century it no longer prefers burnt for attributive use - the two forms are about equally common in this context now.
(Search strings used: "have_INF burned,have_INF burnt" vs. "_DET_ burned _NOUN_,_DET_ burnt _NOUN_".)
Surprisingly, the data for gilded/gilt is much weaker than for burned/burnt.
- Gilded is consistently about twice as common as gilt for attributive use. (The factor is only slightly more than 2 in AE and only slightly less in BE.)
- Unsurprisingly, both variants of English also prefer gilded over gilt when it is unambiguously a verb form (after a form of have), and this preference is stronger in AE than in BE. But surprisingly, this preference is weaker than for attributive use. Even more surprisingly, in BE the specific phrase having gilt is a special exception in that it is several times more common than having gilded!
Fortunately I found the solution to the last mystery: The vast majority of occurrences of having gilt in recent British literature is actually in the exact phrase "having gilt the ocean with his beams" from Shakespeare's Titus Andronicus.
A similarly strong distortion is caused by gilt edges (never: gilded edges) of books. As these were once mentioned so often in catalogues, they tended to dominate attributive use of gilded/gilt for many decades.
Finally, I didn't use it at first because I have no idea how it's implemented, but you can also use the ngram viewer to search for gilded/gilt as an adjective as opposed to gilded/gilt as a verb form ("gilded_ADJ,gilt_ADJ"). The result is for once actually consistent with the above results for burned/burnt:
As adjectives, gilded and gilt are about equally common right now, but until very recently (about 1990), gilt was about twice as common as gilded. The irregular form is only slightly more common in BE than in AE.
Conclusion: Ultimately it looks as if, similar to the case of burnt, the main reason for the inertia of gilt is those cases where it is felt to be an adjective rather than a verb form, gilt edges of books perhaps being the most important.
PS: I just noticed that your question starts with a misunderstanding of language evolution. It's not that every verb went one route or another. A lot of verbs went both routes and then the two forms battled it out between them. Overall, from some point on -ed was considered to be the normal, regular past participle ending. But there seems to have been a phase in the 19th century during which the -t endings appeared to be winning.
What we need to look for, and I have done this above as well as I could, is reasons to prefer one (e.g. regularity) or the other (e.g. tradition), as well as factors that make one or the other of these reasons stronger.