I almost don't bother to post facts on chain and binders anymore because most people here simply want to find someone else to agree with them that going cheap and using unacceptable and unsafe binding materials is okay. I'm sure that you'd find someone here who will rather strongly advise that using your parking brake would be plenty as long as you lock it in four wheel drive. However, since you have not been here for very long, I won't group you with those. As you likely noticed, nylon straps are under no circumstances acceptable to attach a tractor to a trailer. Fraying, sunlight, degrading etc. has positively nothing to do with them not being safe. They will not hold your load, period.
Any grade of chain will be better than nylon straps; period. Also, they do grade chain for a reason. It is not marketing strategy or just for fun. It's sort of like using the right tool for the job. You know, you can likely take nuts off of your tractor with vice grips, but there is a more appropriate tool you can use to do the job properly and it won't really cost you any more. If you don't care if your tractor exits off the rear of your trailer, don't bother using anything at all. If you do care about your tractor, I'd rather strongly suggest you use the right tool for the job. The great thing is that the right tool for the job won't cost you even $50 more than the wrong tool.
If you have a Tractor Supply, Rural King, Lowes, or Home Depot store in your area, you can likely buy some 3/8" grade 70 chain to go along with your 3/8" binders you found. Will the 5/16" grade 70 chain work? Most likely. But, for about $10 more, wouldn't you rather do it right? Heck, you can probably save another $10 from the grade 70 5/16" and get 3/8" grade 30 chain. It too will probably work. It all depends on what you want to accomplish. Since I nearly lost my tractor early last year off of my trailer due to my own stupidity, I took it upon myself to research the subject and buy the proper binding materials since my tractor is worth more than $100. Even if it were not, I'd rather not have to worry about killing someone else because I wanted to save $10.
I don't mean to sound sarcastic, but the laws of physics don't really change much nor do the laws of averages. I posted the physics and equations earlier to enable you to calculate the strength of binding material you should need when taking into consideration the flexing of a 10k and smaller trailer. That equation is not good for figuring the size needed to keep your tractor on your trailer in the case of an accident. I found the equations for that that where you simply enter the weight of your tractor and the speed of the crash. I won't bother to post it here though. No need. Those who want to be safe will and those who want to save $10 will not. At least you are smarter than I was, and you are asking about what material to use. There is plenty of good advice and plenty of bad advice. It's simply your mission to decide which is which and do what you feel best. Either way, you're ahead of the curve for doing your research and asking questions. Good luck!