You probably know most of the below but I'll just throw it out there for anyone else who might have the same problems.
Regarding using heavy threads in machines not really built for it, the first trick is to loosen the lower bobbin a LOT and you usually have to tighten the top tension a lot to get the stitch balanced. Get some thread lube and lubricate the bobbin thread as well. Not all machines can do it at all but some off the shelf ones can accomodate TH69 bonded nylon with the proper tensions and just not going full speed.
When doing zig zags (or you get a small tangle) it's important to realize that stitching the fabric makes it very stiff. When you reverse back over zig zag stitches your needle often hits that hard spot and flexes and will displace sideways and often hit the throat plate or the shock of hitting the hard spot alone can cause parts to scoot along their adjustment rods or whatever in the timing, thus throwing the timing off. Basically, if you get a tangle or are making bar tacks (tight zig zags and then back back over it to double it) go very slow and listen for problems. Few home level machines do this well. I should know, I've burnt up at least a dozen making bartacks.
While not likely the culprit, make sure you are using the right needle size for the thread you are using as well, not just the machines size / format. If the thread just barely squeezes through the needle you are likely to get problems so you need to go up a hole size. There are tons of charts online to help pick the right needle size for your thread. Bigger needles punch bigger holes in thin fabrics, but they can support smoother sewing with thicker threads.
TH69 Bonded nylon is commonly used in outdoor products where tensile strenth is necessary. You can find it in thinner thread which is more friendly to home sewing machines and still retain some of the benefits. Either way, it's hard to get outside of a full pound cone, but it is realiable, strong and holds up to abrasion and uv well. Expect a cone to put you back around $20 bucks. Cotton will just rot in most outdoor applications. Polyester is ok but is more likely to have the color bleach in uv as well as it is usually weaker than nylon and it often frays easier.
If your machine cannot handle thicker threads and you have to resort the hand stitching on thinks like backpack straps or repairing gear that carries a tensile load you can buy just a single pre-wound bobbin of the thicker thread to work with. My company sells individual bobbins as repair equipment for slacklines but they are the exact same thread bobbins that Adventure Medical sells in their survival kits and I'm sure you can find them elsewhere too.