Agreed that load placement can make a huge difference. Good solid racks and having loads shared between the front and rear really help maintain the balance of the bike. But do know that this CX bike is not intended to carry any more then a water bottle, it's for racing not touring or basic transportation. The Bb height and steering geometry are the two bigger aspects that you will never change.

Having said that I do enjoy a senseless mod sometimes So what would I do? If the loaded issues are steering shimmy then stiffening the frame's torsional flex is a big goal. Double TTs don't do much for that as the extra tube isn't in the line of twist. tandems use a internal lateral tube, from the HT to the second BB, to achieve this. For a single think mixte external laterals. Mid way down the back side of the HT to the seat stays just above the drop outs is about the most direct line you can add tubes and avoid the brass lugs and drop outs. (TIG and brass are not friendly to each other).Like a mixte attaching these external laterals to the ST mid way on it's length to further reduce the un supported lengths. This has been done by really smart builders long ago before larger diameter tubing was widely available. But it does significantly change the image of the frame. So many these days would scoff at the results.

Further comments- I note the seat forward position. On a racing inspired with usually not slack STs this means there's more forward weight as well as less upper body sup[port from your core muscles (and less gluts involved in pedaling). Then there's the fairly high and close to the seat bar grip locations. I see a bike set up to achieve a short reach to the bars with a very upright upper body. Not at all what I would call a well balanced position that reduced effective power and increases handling issues. That with a racing handling intention it's no wonder that your loaded experiences are less then ideal.

So play with the frame mods all you want but I doubt you'll be happy after them. Are there reasons why this positioning is the way it is? have you tried other fitting positions? Do you have flexibility or medical limitations we don't yet know about? Have you tried other bike sand if so do they feel better? So many questions and little data to help you choose a path. Andy