Yes, a hot iron would melt olefin. This is an upholstry fabric that does not require pressing, especially when making a cushion.

In tailoring clothes pressing is most necessary, but most upholstry does not need pressing. If you look at your figures 65% of your fabric is synthetic fiber.

I agree, I wouldn't use an iron on Olefin (man-made nylon). If you want nice flat seams you can top stitch the seam down which makes it more sturdy, or run your thum nail over the seams to flatten them.

One more thing if you are new to sewing, safety first. Always keep your fingers away from the needle. It sounds crazy to have to say it but sometimes we can get in a hurry and it's something to be aware of.
Also be careful not to pull the fabric through, just guide it. Pulling can break needles.

Thank you both for the advice, I really appreciate it.

I already have been pulling the fabric through - namely because I was hemming jeans and when you get to the thick part, the feed dogs were not advancing it. Not sure how else I would have gotten around this part other than maybe just handstitching over the seams.

My other discovery was that my machine does not like size 18 needles - I was very frustrated with it, continually bunching on the lower side of the fabric regardless of tension, but as soon as I swapped out the needle to a size 16, it was happy again.

I look forward to starting my first real project - the dog bed cover! I still can't believe the deal I got on this upholstery fabric. thankfully it washed well - I tumble dried it on low, and it came out fine. Washability is key for a dog bed - I hope it stands up over time, but given that I only paid $6 for the fabric, I won't be too upset if my first project doesn't work out. :)

I am probably a little late on the this post. Where you can not use the iron to press olefin if you have a clothes steamer not from your iron it will soften the fabric do not lay it on the fabric like others said use your fingers, hand or even wooden clapper or wooden spoon to flatten or mold near seam. The use steamers in upholstery shops.
Your right about the size of the needle, my Uncle and Aunt had an upholstery business for years, they used mostly 14 and 16 needles. Make sure you adjust your stitch length needs to be 3 to 4 or longer stitch length.
Have you ever heard of a sewing Hump Jumper? It may help on the jeans and other thick layers of fabric. Site shows it below, just lifting the back of presser foot may work.

Here is a link that might be useful: Hump Jumper

Gfoak:

Try a jeans needle and when you get to the seams walk the needle across with the hand wheel. It may be that your machine's motor is not strong enough to sew heavy fabric.