diff --git a/packages/block-editor/src/components/block-list/block.js b/packages/block-editor/src/components/block-list/block.js
index deef2d75386fd5..c44705d3fb7535 100644
--- a/packages/block-editor/src/components/block-list/block.js
+++ b/packages/block-editor/src/components/block-list/block.js
@@ -517,6 +517,7 @@ function BlockListBlockProvider( props ) {
 				__unstableIsFullySelected,
 				__unstableSelectionHasUnmergeableBlock,
 				isBlockBeingDragged,
+				isDraggingBlocks,
 				hasBlockMovingClientId,
 				canInsertBlockType,
 				getBlockRootClientId,
@@ -594,7 +595,9 @@ function BlockListBlockProvider( props ) {
 					blockEditingMode === 'disabled' &&
 					isBlockSubtreeDisabled( clientId ),
 				isOutlineEnabled: outlineMode,
-				hasOverlay: __unstableHasActiveBlockOverlayActive( clientId ),
+				hasOverlay:
+					__unstableHasActiveBlockOverlayActive( clientId ) &&
+					! isDraggingBlocks(),
 				initialPosition:
 					_isSelected && __unstableGetEditorMode() === 'edit'
 						? getSelectedBlocksInitialCaretPosition()
diff --git a/packages/block-editor/src/components/inner-blocks/index.js b/packages/block-editor/src/components/inner-blocks/index.js
index 442f2568ce73dd..5233c063ba2094 100644
--- a/packages/block-editor/src/components/inner-blocks/index.js
+++ b/packages/block-editor/src/components/inner-blocks/index.js
@@ -197,10 +197,9 @@ export function useInnerBlocksProps( props = {}, options = {} ) {
 				__unstableGetEditorMode,
 				getTemplateLock,
 				getBlockRootClientId,
-				__unstableIsWithinBlockOverlay,
-				__unstableHasActiveBlockOverlayActive,
 				getBlockEditingMode,
 				getBlockSettings,
+				isDraggingBlocks,
 			} = unlock( select( blockEditorStore ) );
 			const { hasBlockSupport, getBlockType } = select( blocksStore );
 			const blockName = getBlockName( clientId );
@@ -219,15 +218,13 @@ export function useInnerBlocksProps( props = {}, options = {} ) {
 					blockName !== 'core/template' &&
 					! isBlockSelected( clientId ) &&
 					! hasSelectedInnerBlock( clientId, true ) &&
-					enableClickThrough,
+					enableClickThrough &&
+					! isDraggingBlocks(),
 				name: blockName,
 				blockType: getBlockType( blockName ),
 				parentLock: getTemplateLock( parentClientId ),
 				parentClientId,
-				isDropZoneDisabled:
-					blockEditingMode !== 'default' ||
-					__unstableHasActiveBlockOverlayActive( clientId ) ||
-					__unstableIsWithinBlockOverlay( clientId ),
+				isDropZoneDisabled: blockEditingMode === 'disabled',
 				defaultLayout,
 			};
 		},
diff --git a/packages/editor/src/components/editor-canvas/index.js b/packages/editor/src/components/editor-canvas/index.js
index 3d561a5c01cda4..2a1a1d929663b5 100644
--- a/packages/editor/src/components/editor-canvas/index.js
+++ b/packages/editor/src/components/editor-canvas/index.js
@@ -376,6 +376,10 @@ function EditorCanvas( {
 							: localRef.current?.parentNode
 					}
 					renderAppender={ renderAppender }
+					__unstableDisableDropZone={
+						// In template preview mode, disable drop zones at the root of the template.
+						renderingMode === 'template-locked' ? true : false
+					}
 				/>
 				<EditTemplateBlocksNotification contentRef={ localRef } />
 			</RecursionProvider>