So much could be done! It can be really challenging to accommodate changes to reports as well as keeping it looking good so I feel your pain!
My initial reaction is to do a lot with formatting. For example, do the axes really add information when you have the marks labelled?
I'd also recommend building some regularity in to the design. So at the moment there are rectangles, squares, headers etc. I'd think about literally designing boxes for each part of the data. A bit like tiles; every part has it's own tile. These tiles should have lots of padding. You might choose to have a background colour and a tile colour. This would really neaten it up. It looks like the user has two starting points instead of one. Do you want people to use their controls first or see the headlines? This should influence the layout too. I'd recommend having a side panel with your controls down the full length of the dashboard. Keep them in a vertical layout container and stack them one over the other. That way there is a clear 'control' section and then the user can read the headlines and detail from top to bottom.
Finally, in terms of chart choices, the bubble chart if it stays should definitely have an accompanying tooltip (whether viz in it or not). The items you have circled in red are as you point out not easy to read. It looks like they are percent of totals. One option is to create small bar charts with % labels. These might be ideal as viz in tooltip. The colours here are rendered pointless, so perhaps using length (in a normal, small bar chart) rather than colour might make this more readable.
There may be a few fundamental things I have misunderstood as I do not know your data and purpose of the dashboard, but I hope some of that is helpful.