I'm a big believer in DIY, but this is a tricky subject and deserves some expansion. I've done a fair amount of testing, some of which has been published.
a. Climbing webbing, while very strong stuff, is slightly below the ISAF strength requirement (small issue), stretches when wet (bigger issue), and is weaker and stretchier yet when wet (big issue). I doubt it is suitable for any boat >30 feet. For boats > 40 feet, Dyneema or SS inside webbing is required to control stretch. Remember that climbers use this webbing doubled (loops) from applications exposed to fall impact; it is NOT USED SINGLE because it is not strong enough.
b. Nylon webbing is VERY difficult to sew to strength without a commercial bar tacking machine. No amount of long x-patterns will get you much past 50%. The reason has to do with differencial stretch between the 2 parts preventing equal load distribution. Reinforcement with a 3rd layer helps (it stiffens the webbing, reducing stretch), but this is all beyond the abilities of a DIY that will not be test breaking samples. This is all very different from sewing polyester and more like sewing Lycra. Bottom line: you are very unlikely to sew something stronger than 2000 pounds.
c. While locking climbing biners can be used, most are quite subject to seawater corrosion and will need to be careful maintained and greased. On the other hand, their light weight is an advantage (won't ding the gel coat and they glide more smoothly) that can be worth it. For light users, this can work. The Kong Tango is very nice and does not seem very prone to corrosion.
(Yes, these are sewn, but I pulled many samples to failure before settling on a method. Before I developed the sewing method, I used scaffold knots, which are about 80% strength in this application and much better than most sewing. This is 8.2mm dynamic rope which is UIAA fall-tested with knots as part of the rigging.) These will also exceed the drop test requirements of the new CE standard for tethers.)
The nice thing about DIY tethers is the ability to customize the length; the standard 3/6 split is all wrong for many boats. My recommendation, given the problems with sewing, is either knot the slings and recognize they are lower strength, or use dynamic climbing rope (8mm is best). For jacklines over 30', run Amsteel inside them.
And a lot more discussion:
http://sail-delmarva.blogspot.com/2013/12/dynamic-tethers.html