diff --git a/src/core/public/styles/_base.scss b/src/core/public/styles/_base.scss
index de138cdf402e6..1e8e6c7411e4d 100644
--- a/src/core/public/styles/_base.scss
+++ b/src/core/public/styles/_base.scss
@@ -34,3 +34,12 @@
 .euiPageHeader--bottomBorder:not(.euiPageHeader--tabsAtBottom):not([class*='euiPageHeader--padding']) {
   padding-bottom: $euiSizeL;
 }
+
+// Kibana's body ignores the `margin-right !important` set by react-remove-scroll-bar
+// (used by EUI's focus trap component & prevents page width jumps on full-screen overlays)
+// due to the 100% width/min-width CSS set by Kibana in other places. To work around this, we
+// grab the `--removed-body-scroll-bar-size` var added by the library & manually set `padding`
+// TODO: Use `gapMode` instead once https://github.com/theKashey/react-focus-on/issues/65 is fixed
+.kbnBody {
+  padding-right: var(--removed-body-scroll-bar-size, 0);
+}
diff --git a/src/plugins/embeddable/public/lib/panel/panel_header/panel_actions/customize_panel/customize_panel_action.tsx b/src/plugins/embeddable/public/lib/panel/panel_header/panel_actions/customize_panel/customize_panel_action.tsx
index ec6c2011ca53d..a5d8719b99c99 100644
--- a/src/plugins/embeddable/public/lib/panel/panel_header/panel_actions/customize_panel/customize_panel_action.tsx
+++ b/src/plugins/embeddable/public/lib/panel/panel_header/panel_actions/customize_panel/customize_panel_action.tsx
@@ -129,6 +129,8 @@ export class CustomizePanelAction implements Action<CustomizePanelActionContext>
       {
         size: 's',
         'data-test-subj': 'customizePanel',
+        // @ts-ignore - TODO: Remove this once https://github.com/elastic/eui/pull/6645 lands in Kibana
+        focusTrapProps: { scrollLock: true },
       }
     );
     overlayTracker?.openOverlay(handle);