I like the way you think
If I went the way of the solder (which still looks dubious to me), I would expect the solder to impact the response time of the TC, but otherwise nothing else. A big assumption...
I much, much favor the welding method, just because it's a simpler no-nonsense worry-free approach.
I just have to figure out something, somehow. We've posted links before, to spot welders. There's got to be an easy way to weld thermocouples. Google, here I come.