Sounds kinda like the easiest way to do this would be to allow users to filter by date. Then, the "lower" fp would be the current fp, and the "higher" fp would be second page onwards. The current problem is that, when joining the game, users see fp first, and then generally see second page. Even after all this time, FP is generally not nearly as good as second page, as current memes and funny ****posts can easily get bumped onto fp. So they see second page and they are amazed. Upvotes for all them. Meanwhile, a save that was solidly on FP for the full week would be completely invisible to a user who joins 8 days after its made. 

Giving people options, I feel, is generally better than just overhauling a system based on your opinion (even if i do share it). So allow users to set an option for how recent saves they want to be shown, (ie: forever, 5 years, 2.5 years, 1 year, 9, 6 3 2 and 1 months, and maybe 2 and 1 week. The 1 week option's first page would be like the current fp, but would show only the saves matching your search.

A second option, one that I feel could also be useful, is to allow users to filter saves by their VOTES. This would be 3 boxes (all ticked by default), so you can hide saves you have already seen (such as those you liked, or those you didnt) and then discover what saves are left. This CAN then introduce the problem that people, in an effort to discover more saves, instead of the same ones over and over, may mass downvote saves that dont interest them at all, even if those saves are not bad or objectionable. You may then say "well, they could go upvote saves instead", but that is less likely, as showing only upvoted saves would likely become a substitute for the favorite option. 

Instead of or along with this second option, a companion to the favorite button could be added, "Hide". This allows you to hide saves you dont find interesting from showing up, (although there would have to be an option to show these along with the rest or just show the hidden ones), without having to assign them a vote. 

A third(or fourth kinda) option is the "Blindspot" flag. I sometimes spend a few days playing tons of TPT, and then have midterm projects, final exams, etc, and might be off for a week to a few months at a time. If every time a save got FP (for the first time, since they tend to come and go over their first week), it was given a sort of flag, you could add this as a filter to allow you to quickly catch up on saves you might have missed. The flag can be removed manually by clicking the flag button, or automatically if you vote. Then, if you were away for awhile, you could go through a few pages of what was on fp while you were offline. 

I absolutely think these ideas are pretty good, but I am also certain that there is, in each, an inherent flaw, or a gripe that would be shared by a large fraction of the user base. Being a long time player myself, TPT has gone so far, and while these may improve QoL, they also would fundamentally change how saves are viewed, and that may upset people.

its funny to see people thinking about whats already been added to snapshots so much. although the idea of a blindspot seems interesting to me. BUT you both partly miss the fact that if a save is underrated for a week, it will never be rated. i suggest making it so that the time when a save is removed from the main page is calculated by the formula "date when the save was added to FP + 1 week (or some other period of time)", this way homepages will become an order of magnitude more effective because in this way during the time when FP suffers from bad content the author will only need to post one save with a link to the homepage, and if there is some underrated project on the homepage, this project will be able to be duly appreciated, both helping the author and closing the gap in FP. however, we can talk for a very long time about which algorithm will be the best, because people are different and they like different saves, and the most effective of the possible solutions will be to give people an API with save statistics and a main page interface so that people can make scripts that will have their own FP algorithm.

Some subframe had to be discovered, yes, but not quite as much as you might think.

I don't think layering was discovered, but learned from the code. People who understand the code can do a good amount with the game. It is open source, after all, so we can know what each element does by looking at the code.

Certainly the way FP and things are set up isn't optimal, but I don't know if other options are realistic.