I don't know that adapting the old system is the way to go, coding wise. With big projects at TER's scale, it's almost always easier to implement something from scratch than it is to iterate the existing system.
This is long-winded. If you're lazy, there's a TLDR at the bottom.
It does have to be easy for the reviewer to use, that's a totally fair point, and I would say, X*N/Y is easier to use from the standpoint of you not having to worry about reviews getting declined because you felt you received a 10/10 BBBJ, but TER saying you received a 7/10 BBBJ. That's the source of much confusion and frustration, especially among new reviewers.
From a user point of view (which is the majority of people on TER), the current scoring system is garbage. It's not immediately apparent looking at a review list what 7.9/8.3 even means. I think the X/Y system you're improving is more confusing if you don't know what you're looking at. It's a very poor user experience. I think the star rating system makes much more sense for someone who's going to search for some basic things and select a provider with good pictures provided you can bring up the appropriate list of providers.
Also, the more you reveal about what numbers someone has the worse off you are because the system becomes easier to game (and it certainly is being gamed). I think we'd be good to set 5 stars somewhere around a current 8/8 so any additional ranking would just determine where a provider falls in a "SortBy:rating" or a specific min/max search kind of scenario.
On that topic, Why force a new, paying user to sift through hundreds of providers to find someone?
I think you and I see TER in different states see. You've been here longer and have adapted to how it works. It's perfectly usable as-is, which is basically a bulletin board with some profile functionality added in. You see it as it is, and want it to work better without changing much. What I see TER's real potential in is not necessarily a bulletin board but instead a curation service. You punch in a list of things you're interested in, and tell the site how much you value each thing you're looking for (this can happen simultaneously, like an inverse review), and it spits out a list of providers to your specifications (that is service score(s), distance, price, recently reviewed, etc). Think, "the Yelp of hookers"
Of course, you have to keep and expand on the current system, so the advanced options should always be there and there should be more of them, but if we're going to improve anything, it should probably be the experience of new users. In order to do that, we need data.
(X*N)/Y is a good first step. Changing the default provider lookup criteria would be a good second step (it should be recently reviewed in the last couple months, accurate pictures, sorted by overall rating. Currently it defaults to date, which isn't useful by itself) and having some sort of recommendation engine would be a good endgame.
Existing data would have to be ported over, which shouldn't be too hard to at least have a weighted starting score to kick things off. Like you had N reviews with an average of X score, so that counts towards Y reviews at your average in the new system to start and it'll go up/down from there.
TLDR
The idea here is to abstract the rating system from the numbers, and provide additional detail about the quality of specific services. Then use the new abstract system to improve user experience, with a focus on new paying members.
This adds additional value to the site, makes the review system harder to game, reduces the pressure on a reviewer to only give perfect scores, reduces the pressure on providers to only have perfect scores and gives a concrete method of enforcing authentic reviews.
