MAX7219 Alternative for 4 Digit 7-Segment display.

What is wrong with driving continuously? You just write to the shift register once and the data stays there.
You can also set up the shift registers to be independently loadable (common data, common shift clock, separate load clock, 6 pins total vs 3 with SPI) and just update 1 digit at a time like you would do with the 7219/7221.