Storing Data in DNA [pdf]
homes.cs.washington.edu
homes.cs.washington.edu
But there are lots of natural techniques to copy dna and repair it when it fails to copy properly so durability should be solid.
"Progress in DNA storage has been rapid: in 1999, the state- of-the-art in DNA-based storage was encoding and recovering a 23 character message [7]; in 2013, researchers successfully recovered a 739 kB message"
That's not a terribly large message. The difficulty of synthesizing large tracts of DNA reliably is a major bottleneck. It was a huge accomplishment when a full, relatively small genome (1x10^6 bases, humans are ~3x10^9) was synthesized in 2010 [1]. Granted for storage purposes, fully synthetic DNA may not be required, but it's still hard to assemble pre-existing DNA into very large constructs.
Sequencing the message itself is on its surface not too hard, I think a current-gen high throughput sequencer can read up to 2 trillion bases in a single run. It's not super fast (1-2d turnaround), or random access though, and the random access nature is one of the innovations in the paper. Still some sequencing approaches are a little quicker it should be possible to leverage modern sequencing tech to make this suitable for archive-level purposes.
Other thoughts on the paper: they have a cool take on how to avoid errors (Huffman code), and take advantage of highly parallel DNA synthesis approaches by properly segmenting the data they want to store into useful chunks. You still have to avoid errors in synthesis and replication for DNA storage, and they take steps to mitigate risk there.
Anyway, cool paper, if anyone knows more about the state of the art of long-DNA strand synthesis I'd love to hear about it!
I think yours is probably the right way, though.
Houseplants are substantially harder for a variety of biochemical reasons including having multiple chromosomes, and more difficult selection protocols, but yeah that should be possible too and made somewhat easier by CRISPR.
I imagine impementing some kind of additional checks - e.g. special genes that kill organisms wih a bad checksum of the stored data.