I was able to finally solve this after A LOT of searching and testing. In order to fix this, I simply replaced each double-quote with two double-quotes. Having two double-quotes treats the double-quote as an 'escape value'... which I guess means that the double-quote is not treated like a closed quote.
This might be a SQR specific solution.
Simplified code solution:
Let $asset_descr = '"' || Replace(&dep_asset.descr, '"', '""') || '"'
Let $string = $asset_descr
Write 1 from $string