Well Google is making more me convinced each day with my investment in kagi $10 subscription. Kagi native support for archive wayback is one of the most useful features for me.
But you probably can somehow move the link to a more prominent position as Kagi does support custom css that is served with your search results. [2]
1 https://help.kagi.com/kagi/features/website-info-personalize...
2 https://help.kagi.com/kagi/features/custom-css.html#customiz...
Yeah. it's worth a few bucks.
[1] https://help.kagi.com/kagi/search-details/search-sources.htm...
They say that what makes them usable, their results most topical, is their own index.
They also list Google as an ancillary, as well as many others.
But the "feel" is more from the UI, and the relevance of the results. Both of these ways Google completely fails on now.
I didn't realize it was a rebalancing. But seriously, I have no regrets. if nothing else, the incentive alignment matches my values better.