That's an interesting, and clever approach! Some of it is probably over my head.
You'll want to keep in mind that Trace Bitmap is not designed to precisely duplicate raster images in vector form. Depending on how small the original image is, and also on the complexity and quality of the image, you could even see small descrepancies at 100% zoom. The larger the original, the better. And the less complex the original, the better. Very thin lines might not display very well. (I'm not sure if "pen ball designs" means ball point pens drawings???)
Yes (agreeing with Moini), File menu > Export PNG is the best option. I don't think you will see any noticable difference between the vector version and the new PNG version. However, as I mentioned, you might see some difference between the original raster and the new vector version. If the originals are 5520x4144 pixels, you probably won't see much difference.....although if it's ball point pen drawing, I'm just not sure.
I guess you can only try it and see what happens though.
Just out of curiosity though, isn't 7632x6480 pixels way bigger than a tshirt, and any of the other products you mentioned? It seems like the original size you mentioned (5520x4144) would be big enough? (This is the part that's probably over my head.) I just did a very quick and very rough calculation, and 7632x6480, at 96 dpi, is a little over 6 feet x 5 feet.