Not exactly a new idea, but one that I find delightful and have never seen anyone else use. I first learned of this idea from Rose in The Cake Bible - a thin round of biscuit as the base and even the sides, if you wish. Not biscuit as in *baking powder biscuits* but the French word (bis-kwee), the thin sponge which is baked in a 1” high sheet pan and most often used to create rolled cakes with filling.
Might not work for every style of cheesecake you make, but there are many different flavours possible to mix and match with your cheesecake fillings. There’s the usual almond-flavoured, often called jaconde. Rose has a recipe for that as a variation of a plain vanilla biscuit in TCB. Other variations, too, and you could come up with more yourself. She used the almond one as a base for her Golden Glory Cheesecake, and I’ve used it as a base and layers for opera-style cakes. Have used the ginger variation as a base for one of her lighter butter cakes (the Golden Luxury), when that was the best way to work the bride’s desire for “ginger somewhere” into the flavour profile of her lemon wedding cake. It was delicious! And so unique.
Check out Rose’s note on p 142 TCB, where she talks about this (cutting it with scissors, etc.). As she says, a sheet of biscuit has many possibilities. I like to have some on hand in the freezer at all times. Have even cut cake decorations from it - small stars that looked so nice on top of a ganache-covered birthday cake. And bonus! you can use it to line the parchment-lined bottom of your pan before pouring in the batter, where it will help enormously with the release when it comes time to remove the cake from the pan. (Or you can bake the cake as normal and unmold on to a round of biscuit sitting on a cardboard cake round.) Another bonus is that the biscuit base nicely absorbs any excess moisture.
Also check out Rose’s notes p 82 for tips on unmolding cheesecake. Are you using parchment? That would help. Also the usual running a thin spatula around the sides, placing the pan on a heated burner for 10 to 20 seconds, moving back and forth, and then invert. Reinvert, if desired.
Last but not least, check out her unmolding tips and all the ways in which Rose has handled the base, its release, etc. in her newest book, Rose’s Heavenly Cakes. Cheesecakes pp 242 - 260.