I've made 4" tarts in my baking business, I use 4" 'english muffin' rings, but you could basically use your mini springforms the same way.

You don't need bottoms, just use one hand to press the crust into the ring while you use the other hand to keep it steady on the baking sheet. (Most people use parchment lined sheets, I don't. It adds up to more scrubbing at the sink but I'd rather do that and save the money and paper...but depending on your recipe, you may prefer to use it).

When finished, you can run a small spatula or knife around each cheesecake and slide the ring right off. You may have to rinse the rings between batches, but believe me, it is much less hassle than dealing with little strips of paper sticking everywhere. Also, before I figured out that I didn't need the paper, I had to butter the rings to get the paper to stick, and then butter the paper.

If the crust has enough fat in it (and most recipes do), this is not necessary.

Line a rimless baking sheet with foil or parchment and place the springform rings (sprayed or greased lightly) on top. Pat the crumb crust firmly and thickly into the rings, to a level just above the groove, then add the filling and bake. If you don't have a rimless baking sheet, turn a rimmed sheet upside down. When the first batch is done, slide the cheesecakes--still on the foil--onto a counter and allow to cool before removing the rings. If the filling is less that an inch high, you could probably remove the rings after 10 minutes without fear of the cheesecake flattening.

I've not done this for cheesecakes larger than 3" but it's worked for me when I've had to mass-produce shamrocks (key lime cheesecake) and cheesecake petits fours for Mother's Day with cookie and canape cutters: Bake the cheesecake in a rimmed cookie sheet, chill it, and use metal cookie cutters to cut the sheet into the desired shapes. Depending on the shape you want, there will be a little or a lot of waste, which you can use to make parfaits. Be sure to dip the cutters into hot water and blot on a towel before making each cut, and to cut the shapes before adding a topping.

I've used jumbo cupcake liners--the ones for big giant muffin pans--to line my heart-shaped mini cake pans. I center the liner in the pan and hold it in place with one hand while using a finger from the other hand to crease the liner into place along the bottom of the pan. As soon as they're done baking, I pull the cakes out of the pans to cool so that I can get the next batch in the oven. Theres something about the folds that makes cupcake liners easier to shape than plain parchment paper, and there's no reason it wouldn't work in place of your springform bottoms.

I've make cheese cakes all the time I line the pan with tin foil and when the cake is good and chilled you can remove it and peel off the foil

I think if you had some heavy foil pie tins you could cut the bottom out to fit inside your springform to cover the bottom plate. I've formed a collar using parchment paper folded several times to line the inside of my springform walls so I could later add toppings that needed to set up without using the springform walls for support . I just tucked one end of the folded parchment inside the fold of the other end and trimmed the base as needed a little. It worked well. I didn't remove the cake from the pan while it was still hot, though.

Could you line with foil? It would be easier to remove.

I don't know if this would work for a cheesecake, but here's what I do with cakes I bake in the springform pan:

Transfer to a cooling rack. Run a knife along the edges of the cake to loosen it completely from the sides of the pan. Wait until it has cooled completely, then slide a long thin spatula between the cake and the base. Use a large spatula to then move it to a serving plate.