Regarding the Tethering Agent (String)
You are prudent to have perused a copy of FAR 101, but it does take a bit of verbal contortioning to read it. If you reduce the gobbledegook that ends at para 101.1(a)4 to plain English, you'll find that this law does not apply to any unmanned balloon carrying a payload that does not exceed the 4 limits in paragraph (i) - (iv). One of those stipulates a maximum "impact force" of 50 lb to separate the balloon from the payload string. Evidently you've succeeded in navigating that tortuous route.
The operative term here, as EOSS reads it, is "impact", which we infer to mean the rapid application of kinetic energy rather than the gradual application of tension which is conventionally used to measure the "tensile strength" of a support member. In other words, a line rated at 50 lbs. tensile strength is capable of supporting a 50 lb static load, but it most certainly will break if that 50 lb load is suddenly accelerated to a speed typical of an aircraft in flight. And we read this limit as it might be applied in the latter case. Thus if one assumes that a payload string struck by an aircraft traveling at a modest 120 kt true airspeed might experience a peak acceleration of 30 Gs, then this 50 lb "impact force" limit translates to a tensile stress of 1500 lb. So in that sense, the 260 lb line that Chris and EOSS have used is well within the stipulated limit, even for the light payloads that we fly.