I don't know how big the original is, but since you're using a mac: in Preview you can use the tools>annotate>signature to 'sign' electronically (if you haven't recorded an electronic signature there, you'll have to use the manage signatures option under signature to do so). Advantage of doing so is it doesn't change the size/composition of the file much.
*The instructions in the online oath invitation specify you can do this, although it looks like the instructions are for (an older version of) acrobat reader. I just tested it with acrobat reader and it's basically the exact same functionality, but (ignoring the IRCC instrctions because outdated) in Acrobat you have to use the "E-Sign" menu, but it works exactly the same as Preview. (Could IRCC care or check that you used preview? I dont know)
IRCC says you have to take a picture of your signature and copy/insert that (rather than draw with a trackpad or mouse). I don't know how they'd be able to tell but both programs have that camera functionality (I think, too lazy to check reader).
I did a test with Acrobat and it came out as 300kb instead of your 1000kb, I guess because not scanning/compressing the text.
If, of course, you feel like trying again.