Adding the caps on the back shouldn’t be too much of a problem. I’ll also change the signal traces to 8mil and I guess 10 for all of the power traces?
I’ll give an opposite opinion here . . . I dislike your skinny tracks immensely, they so look fragile to my eye, if you have to do any re-work on the through hole parts or even the SMD ones and you don’t have good tools you risk pulling tracks off as they will heat up very fast due to tiny thermal mass.
You should also add a plane to the top layer (I assume you have one on the bottom layer) to avoid warping.