I found that it is possible to rearrange the UI by using scripts, and I have implemented what I suggested above: pack most UI buttons into a control panel of sorts. This works well for me, solving the unstable mouse interaction with the auto-hiding and overlapping toolbars.
This is a script that sets my VR "cockpit". It assumes the UI is configured to a resolution of 1200 (I believe it's the default). I typically fly with the Camera toolbar hidden, but I added it here for those who use it.
// Rearranges SE's UI into a control panel that is more comfortable to use in VR
// Author: Anton G. Alvedro (galvedro)
Set ShowVelocityVector true
Set EnableLensFlares false
Set EnableLensGhosts false
Set VRInterfaceCopies 1
Set VRMoveDirection 0
ShowDialog "Main toolbar"
ShowDialog "Filters toolbar"
ShowDialog "Navigation toolbar"
ShowDialog "Camera toolbar"
// NAVIGATION TOOLBAR
SetWidgetStyle "Navigation toolbar" { WinColor (0,0,0,0) PosPix (368,966) }
SetWidgetStyle "Navigation toolbar|Pin" { PosPix (2000,2000) }
SetWidgetStyle "Navigation toolbar|Decrease velocity" { PosPix (2000,2000) }
SetWidgetStyle "Navigation toolbar|Increase velocity" { PosPix (2000,2000) }
SetWidgetStyle "Navigation toolbar|Free mode" { PosPix (240,36) }
SetWidgetStyle "Navigation toolbar|Spacecraft mode" { PosPix (272,36) }
SetWidgetStyle "Navigation toolbar|Aircraft mode" { PosPix (304,36) }
SetWidgetStyle "Navigation toolbar|Go to object" { PosPix (356,36) }
SetWidgetStyle "Navigation toolbar|Land on object" { PosPix (388,36) }
SetWidgetStyle "Navigation toolbar|Center object" { PosPix (420,36) }
SetWidgetStyle "Navigation toolbar|Track object" { PosPix (452,36) }
// FILTERS
SetWidgetStyle "Filters toolbar" { WinColor (0,0,0,0) PosPix (0,0) }
SetWidgetStyle "Filters toolbar|Pin" { PosPix (2000,2000) }
SetWidgetStyle "Filters toolbar|Filter settings" { PosPix (2000,2000) }
SetWidgetStyle "Filters toolbar|Spacecraft#plural" { PosPix (352,1040) }
SetWidgetStyle "Filters toolbar|Galaxies" { PosPix (384,1040) }
SetWidgetStyle "Filters toolbar|Stars" { PosPix (416,1040) }
SetWidgetStyle "Filters toolbar|Clusters" { PosPix (448,1040) }
SetWidgetStyle "Filters toolbar|Nebulae" { PosPix (480,1040) }
SetWidgetStyle "Filters toolbar|Planets" { PosPix (512,1040) }
SetWidgetStyle "Filters toolbar|Comet tails" { PosPix (544,1040) }
SetWidgetStyle "Filters toolbar|Atmospheres" { PosPix (576,1040) }
SetWidgetStyle "Filters toolbar|Clouds" { PosPix (608,1040) }
SetWidgetStyle "Filters toolbar|Water" { PosPix (640,1040) }
SetWidgetStyle "Filters toolbar|Aurora" { PosPix (672,1040) }
SetWidgetStyle "Filters toolbar|Constellations" { PosPix (704,1040) }
SetWidgetStyle "Filters toolbar|Orbits" { PosPix (736,1040) }
SetWidgetStyle "Filters toolbar|Markers" { PosPix (768,1040) }
SetWidgetStyle "Filters toolbar|Labels" { PosPix (800,1040) }
SetWidgetStyle "Filters toolbar|Selection pointer" { PosPix (832,1040) }
SetWidgetStyle "Filters toolbar|Velocity vector" { PosPix (864,1040) }
SetWidgetStyle "Filters toolbar|Celestial grids" { PosPix (896,1040) }
// MAIN TOOLBAR
SetWidgetStyle "Main toolbar" { WinColor (0,0,0,0) PosPix (0,0) }
SetWidgetStyle "Main toolbar|Pin" { PosPix (2000,2000) }
SetWidgetStyle "Main toolbar|Display" { PosPix (2000,2000) }
SetWidgetStyle "Main toolbar|Main menu" { PosPix (464,1072) }
SetWidgetStyle "Main toolbar|Wiki" { PosPix (496,1072) }
SetWidgetStyle "Main toolbar|Universe map" { PosPix (528,1072) }
SetWidgetStyle "Main toolbar|Solar system browser" { PosPix (560,1072) }
SetWidgetStyle "Main toolbar|Solar system chart" { PosPix (592,1072) }
SetWidgetStyle "Main toolbar|Star browser" { PosPix (624,1072) }
SetWidgetStyle "Main toolbar|Find object" { PosPix (656,1072) }
SetWidgetStyle "Main toolbar|Spacecraft manager" { PosPix (688,1072) }
SetWidgetStyle "Main toolbar|Journey log" { PosPix (720,1072) }
SetWidgetStyle "Main toolbar|Locations" { PosPix (752,1072) }
SetWidgetStyle "Main toolbar|Settings" { PosPix (784,1072) }
// CAMERA TOOLBAR
SetWidgetStyle "Camera toolbar" { WinColor (0,0,0,0) PosPix (430,1104) }
SetWidgetStyle "Camera toolbar|Pin" { PosPix (2000,2000) }
SetWidgetStyle "Camera toolbar|Camera settings" { PosPix (2000,2000) }