You are not the only customers who want to replace EPCS/EPCQ devices with Cypress SPI Flash. Unfortunately, it is not a straightforward drop-in replacement in most cases. However, we have heard many successful cases, especially with 128Mb or lower density devices.
In your case, since you require 1Gb device, it may be a little more difficult, but I would not say it is impossible. You may need to do some customizations in your development environment such as disabling EPCS ID check from the Quartus II tool, making sure your configuration code does not cross the die boundary inside this 2-die stack of FS01GS, etc.
Furthermore, you may try to ask Altera/Intel for technical support for 3rd vendor configuration devices. Depending on your application, they may support you to use Cypress devices. For example, if your application is for automotive, it is likely you will get support from them.
In conclusion, S70FS01GS is not fully compatible with EPCQL1024F24IN but if you are willing to customize your design, it may be possible to replace it. If you can spend a little time to do a quick feasibility study on your system, it may be worthwhile. Cypress technical support is also a good resource you may use if you encounter some specific issues while doing your development. You may open a case and we will give you our best support.