Project requires 4 analog pinouts
Can you re-phrase that? Uno has zero analog outputs...
You require one digital output to drive your strip. Don't know what else you need yet.
Maybe you could consider attiny84. It's almost the same as attiny85 but with more pins. You would need to reduce the compiled sketch size to below 8192 bytes for either '85 or '84. That might not be impossible. Post your code. We might spot some ways to shrink it. Also you could try switching on Link Time Optimisation (LTO).
There are other ways to move to a circuit board while still using the same chip. Nano 3 and Pro Mini both use the same chip as Uno. Or you can use a bare atmega328 chip. If 8MHz is fast enough (which is true for almost all projects) then you may not need a crystal+caps.