Maybe...

ui/build-aux/start-breezy-desktop.sh

@@ -0,0 +1,34 @@
+#!/usr/bin/env bash
+
+IFS=: read -ra host_data_dirs < <(flatpak-spawn --host sh -c 'echo "$XDG_DATA_DIRS"')
+
+# To avoid potentially muddying up $XDG_DATA_DIRS too much, we link the schema paths
+# into a temporary directory.
+bridge_dir=$XDG_RUNTIME_DIR/dconf-bridge
+mkdir -p "$bridge_dir"
+
+HOST_XDG_DATA_DIRS=""
+
+for dir in "${host_data_dirs[@]}"; do
+  if [[ "$dir" == /usr/* ]]; then
+    dir=/run/host/"$dir"
+  fi
+
+  schemas="$dir/glib-2.0/schemas"
+  if [[ -d "$schemas" ]]; then
+    bridged=$(mktemp -d XXXXXXXXXX -p "$bridge_dir")
+    mkdir -p "$bridged"/glib-2.0
+    ln -s "$schemas" "$bridged"/glib-2.0
+    HOST_XDG_DATA_DIRS="${HOST_XDG_DATA_DIRS}:${bridged}"
+  fi
+done
+
+# We MUST prepend the host's data dirs BEFORE the Flatpak environment's own dirs,
+# otherwise data (such as default values) load in the wrong order and would then
+# incorrectly prefer the Flatpak's internal defaults instead of the host's defaults!
+if [[ ! -z "${HOST_XDG_DATA_DIRS}" ]]; then
+  XDG_DATA_DIRS="${HOST_XDG_DATA_DIRS:1}:${XDG_DATA_DIRS}"
+fi
+
+export XDG_DATA_DIRS
+exec breezydesktop "$@"

ui/com.xronlinux.BreezyDesktop.json

@@ -13,9 +13,10 @@
         "--device=shm",
         "--talk-name=ca.desrt.dconf",
         "--filesystem=xdg-run/dconf",
+        "--filesystem=host:ro",
         "--env=DCONF_USER_CONFIG_DIR=.config/dconf",
         "--env=GIO_EXTRA_MODULES=/app/lib/gio/modules/",
-        "--env=GSETTINGS_BACKEND=dconf"
+        "--talk-name=org.freedesktop.Flatpak"
     ],
     "cleanup" : [
         "/include",
@@ -55,6 +56,20 @@
                 }
             ]
         },
+        {
+            "name": "scripts",
+            "buildsystem": "simple",
+            "build-commands": [
+                "install -Dm 755 start-breezy-desktop.sh /app/bin/start-breezy-desktop"
+            ],
+            "sources": [
+                {
+                    "type": "file",
+                    "path": "build-aux/start-breezy-desktop.sh"
+                }
+            ]
+        },
+
         {
             "name" : "breezydesktop",
             "builddir" : true,
@@ -62,7 +77,7 @@
             "sources" : [
                 {
                     "type" : "dir",
-                    "source" : "./"
+                    "path" : "."
                 }
             ]
         }

ui/data/com.xronlinux.BreezyDesktop.desktop.in

@@ -1,6 +1,6 @@
 [Desktop Entry]
 Name=breezydesktop
-Exec=breezydesktop
+Exec=start-breezy-desktop
 Icon=com.xronlinux.BreezyDesktop
 Terminal=false
 Type=Application