Publishing trusted assertions would be great because we can cache them on the client in the same way we cache everything else and use Nostr REQ requests to see if updates are available as users navigate.
All clients do that already for Kind 0 (to get user's name/picture). It is very easy to just add a new kind to that same request and get the scores as well. And since these are replaceables, they update only when needed (when the score actually changes, which is rare) and the EOSE can be used to only request for changes since the last event, avoiding the data use of downloading the info for the same user over and over again because we don't know if they have changed or not in the server via other methods.
I will be adding them to Amethyst next, so if you publish it, let me know because I just need to allow users to set up the WoT trusted provider to your pubkey and then they will see the scores in their interface.
The search interface needs an API, though. So, we might need to define the inputs and outputs in a NIP. This could be via http calls, like how blossom does, via DVMs or via NIP-50 itself (user auths and sends a search that uses the WoT of the authed user).