Definitely agree about flushing the carbon filter. A warning about that is on the Chris Coffee website page for the filter and is in the instructions that came with the filter. I don't know anything about the internal structure of the Vivaldi, but those little carbon particles can damage or cause havoc with certain machines -- they can get stuck in check valves, gicleurs, etc.
If you didn't flush the filter before you used it, I would flush several gallons through your machine without the filter to try to get that stuff out. Then flush several gallons through the filter into a bucket or drain and hope for the best.
All that said, I'm suspicious about your TDS readings. AFAIK, carbon particles from the filter won't dissolve in water. Is there a run of metal pipe between the point where you've measured the TDS of the water supply and the filter? If so, minerals might be leaching from that pipe. As for the boiler water, I've seen %TDS go up in boiler water due to evaporation, or it could be minerals leaching off the inside surface of the boiler if it's made of copper.
It's conceivable that your softened water is slightly acidic and it's etching minerals off of any metal it comes in contact with. Doesn't seem likely with the high TDS you have (it's not an RO system, is it?) Even so, you might want to get some pH test strips to check that out.
I'm wondering if your TDS meter is working correctly, and if you're using it correctly. For one thing, I believe you're not supposed to measure hot water. You have to let it cool first.