How to connect to Yandex.Maps your own layer made in the EPSG:3785 projection?

Question

Google Maps

Good afternoon.
The GDAL library has a gdal2tiles.py script that allows you to cut images into tiles using anchor points (normal GPS coordinates).
However, the entire internal kitchen (translation of coordinates, etc.) of this script is tied to the Google projection EPSG:3785 .
At the same time, it is clear that Yandex.Maps uses the EPSG:3395 projection .
Which in the end gives an unpleasant surprise - the numbers of tiles in EPSG:3785 and EPSG:3395 simply do not match.
For example, the tile at this coordinate [54.99412, 38.026884] ( Link ) has the following tile addresses:

Vendor	Projection	Z	X	Y	Link to tiles
Yandex	EPSG:3395	17	79381	41576	Link
Google	17	EPSG:3785	79381	41461	blob:https%3A//www.google.ru/d8dd7055-2953-4345-82bd-8e3f12b951c3 (Google is smart, but you can see it here )
OSM	17	EPSG:3785	79381	41461	Link
gdal2tiles	17	EPSG:3785	79381	41461	Honestly

Actually, the offset identified.
It is clear that this is due to the fact that Yandex.Maps uses a spheroid (EPSG:3395) , while Google, OSM, and gdal2tiles use a sphere (EPSG:3785) .
By itself, I saw this section about custom maps and generated tiles through this program for cutting tiles. But it works on the desktop, not on the server.
What you need is a server solution. At the same time, it is quite nice to have one set of tiles with the ability to recalculate the coordinates of tiles for different projections on the client:

• In the case of Google, OSM - leave as is
  
• In the case of Yandex.Maps, recalculate the coordinates of the tiles.
  

That's the whole subject.
Maybe there are some ready-made solutions, libraries, at least something?

Answer 1

In the Yandex.Maps API, you can connect layers in any projection. And even several layers in different projections at the same time.
https://tech.yandex.ru/maps/doc/jsapi/2.1/ref/ref...
https://tech.yandex.ru/maps/doc/jsapi/2.1/ref/ref...