Well, it was a matter of time.
As of a couple days ago, our submission form officially allows the submitter to report an alternate timing method or optimization metric, such as in-game time or score! You can now see titles like
#1312: ikuyo's PC Sayonara Wild Hearts "maximum score" (2,116,350) in 48:23.136 or
#4444: (a lot of author)'s N64 Super Mario 64 "120 stars" in 1:14:04.444 (Console Timing)
Here's also an example of this information in the submission queue (image sourced from a development build of the site)

While we have officially allowed TASers to use whatever metric they want as an optimization target, this decision was not reflected in the way we display submissions and publications on the site, most notably in publication titles and YouTube encode titles. This has been a historical source of confusion, leading to several communities assuming we don't support in-game timers at all, or even causing casual audiences to assume TASes are slower than their real time counterparts.
You will find both a drop-down to select the metric or timing used in the movie, and a field to type how it should be displayed. This information will be used to fill the title data for the movie wherever needed.
If you plan to use this feature, we recommend you explain to us how to calculate or measure the reported metric if it is not obviously apparent, such as when using real time speedrun metrics. This will make it easier for judges or anyone unfamiliar with the game's speedruns to know what to look for.
By the way, if you have or know of a publication that you would like to use an alternate timing method, we have opened a thread for
Publication timing/score update requests, as it can only be changed by people with editing permissions. Keep in mind that this could take us a while, as we are as usual working on a lot of things. Also, this feature is likely to get further revisions and changes in the future, as we find more cases that could use it. Thanks for your patience, and happy TASing!