Keep in mind that the BMPCC 6K can only record 6K in BRAW. It can't do 6K in ProRes formats or output 6K through HDMI (HDMI output maxes out at 1080p60).
You can basically go either route for around the same amount of money. The BMPCC 6K is around $2,000 and the Panasonic CX350 is around $3,700, so that leaves you around $1,700 for a decent lens if you go with the BMPCC 6K. Both of those options will perform much better in lower light compared to the Blackmagic Studio Camera HD and lens combo you have now. Even a BMPCC 6K with an f/6.3 lens will probably look way better.
However, if you can invest in some lighting that would ultimately be your best bet. A camera is only as good as the light it sees. So you may want to consider investing part of your budget into lighting and then swing for a cheaper camera/lens combo. IMO, that will return better overall results than just upgrading your camera/lens.