Um, you only mention the harsh sound on streaming but not from other sources. If you’re not getting that problem from other sources, I'd say it's a streaming issue, not a speaker issue. Your streaming through a Sony BDP, what happens when you play disc? If the disc sounds OK, then it's likely streaming from maybe an mp3 file or maybe the service itself is nobbling the resolution, either will sound tinny compared with CD res or higher resolutions. If the disc sounds the same as streaming, it may be the DAC or some issue with the digital cable, can you try coax vs optical? There shouldn't be a major difference but may reveal a cable fault.
I agree with comments that speakers (and their passive cables) are generally the weak link in audio systems. Probably 90% of the time, you will not hear component upgrades because of this. Cables and deteriorated connections can IME make very distinct differences to the sound. Some speakers do best on zip chord while others do best on twisted or braided pair or quad, depends on the cable capacitance they are designed for. Major reason for the wars on this issue.
On the other hand, if the speakers are older than 10 years, the crossovers caps may have drifted out of spec and need replacing. Ribbon tweeters, can be overdone & sound harsh, great clarity if balanced well though. I like soft domes, seems a safer option to me. That said, I have experienced harsh sound form soft domes (ProAc EBT) on short (1m) thin cables. Upgrading the cable gauge, (same length) improved that and a more normal length was better still. Yeah, I know the cables don't matter crowd, I used to be sceptical on that too but trialling this proved to me that it can matter very much, though sometimes not so much. Like many things the answer seems to be "well it depends".
Anyway, best of luck.
Ken
