There are two ways to solve your problem. One is to get a faster processor. The other is to write more efficient code. This is a very common issue for the whole IT industry. Writing code takes a lot of time and costs a lot of money, even in countries that do not pay their programmers so well. Writing efficient code takes expert programmers, and they get paid more. Hardware is relatively cheap. Hence the decision is easily made, and programmers that are expert enough to write efficient code are a dying breed.
But in the Arduino world, people code as a hobby and don't attach such a high value to the time they spend coding.
Writing efficient code often means making use of features that are specific to a platform, such as avr microcontrollers. Also accessing the hardware directly, not via an abstraction interface. For example, the Arduino function digitalWrite() is much slower than accessing the "PORTx" hardware register directly. But if you access the port directly, then your code cannot be easily moved to another platform later, because the underlying hardware is different, whereas digitalWrite() will probably work without alteration.
If you want a faster version of the Nano, you will almost certainly have to make the move from 5V logic to 3.3V. There is lots of choice. Teensy 3.x, Maple Mini, esp8266 for example. For maximum Arduino compatibility, it may be wisest to choose one based on the microcontroller used in the newer Arduino models "Zero" and "M0" which is the SAMD21 chip. Both AdaFruit and Sparkfun sell Nano-like boards based on this chip. There are also SAMD21 boards on eBay branded "Wemos". But the brand name "Wemos" appears to have been stolen, because these boards do not appear on Wemos' official website. They are not cheaper than some of the AdaFruit/Sparkfun offerings, so I can't see any reason to recommend them.