Meu aplicativo possui os seguintes parâmetros:

android {
    compileSdkVersion 23
    buildToolsVersion "23.0.2"

    defaultConfig {
        applicationId "de.munich.myApp"
        minSdkVersion 17
        targetSdkVersion 23
        multiDexEnabled true
    }

    buildTypes {
        debug {
            debuggable true
        }
        release {
            minifyEnabled false
            shrinkResources true
            proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.txt'
        }
    }
}

Incluí o pacote de suporte v7:

dependencies {
    compile 'com.google.code.gson:gson:2.4'
    compile 'com.android.support:appcompat-v7:23.2.0'
    compile 'com.google.android.gms:play-services:8.4.0'
    compile 'com.android.support:design:23.2.0'
    compile 'com.android.support:recyclerview-v7:23.2.0'
    compile 'com.android.support:cardview-v7:23.2.0'
}

E agora eu tento iniciar meu aplicativo em um Galaxy Ace com a versão 4.4.2 do Android (nível de API 19) e recebo muitos erros porque alguns métodos mencionados no android.support.v7 não foram encontrados:

Could not find method android.view.Window$Callback.onSearchRequested, referenced from method android.support.v7.internal.view.WindowCallbackWrapper.onSearchRequested
Could not find method android.view.Window$Callback.onWindowStartingActionMode, referenced from method android.support.v7.internal.view.WindowCallbackWrapper.onWindowStartingActionMode
Could not find method android.content.res.TypedArray.getChangingConfigurations, referenced from method android.support.v7.internal.widget.TintTypedArray.getChangingConfigurations
Could not find method android.content.res.TypedArray.getType, referenced from method android.support.v7.internal.widget.TintTypedArray.getType

Claro que o aplicativo trava.

Existe alguma maneira de resolver esses problemas sem precisar aumentar ominSdkVersion?

EDITAR

import android.app.Notification;
import android.content.Context;
import android.support.v4.app.NotificationCompat;

public class HelperNotification {

    /**
     *
     * @param context
     * @param title
     * @param message
     * @return
     */
    public static NotificationCompat.Builder buildNotification(Context context, String title, String message) {
        NotificationCompat.Builder builder = new NotificationCompat.Builder(context);

        builder.setContentTitle(title);
        builder.setContentText(message);

        int defaults = 0;
        defaults = defaults | Notification.DEFAULT_LIGHTS;
        defaults = defaults | Notification.DEFAULT_VIBRATE;
        defaults = defaults | Notification.DEFAULT_SOUND;

        builder.setDefaults(defaults);

        return builder;
    }
}

EDIT 2

I/dalvikvm: Could not find method android.os.UserManager.getApplicationRestrictions, referenced from method com.google.android.gms.common.zze.zzaq
W/dalvikvm: VFY: unable to resolve virtual method 1747: Landroid/os/UserManager;.getApplicationRestrictions (Ljava/lang/String;)Landroid/os/Bundle;
D/dalvikvm: VFY: replacing opcode 0x6e at 0x0012
E/dalvikvm: Could not find class 'android.app.AppOpsManager', referenced from method com.google.android.gms.common.zze.zzb
W/dalvikvm: VFY: unable to resolve check-cast 35 (Landroid/app/AppOpsManager;) in Lcom/google/android/gms/common/zze;
D/dalvikvm: VFY: replacing opcode 0x1f at 0x000e
I/dalvikvm: Could not find method android.content.pm.PackageManager.getPackageInstaller, referenced from method com.google.android.gms.common.zze.zzi
W/dalvikvm: VFY: unable to resolve virtual method 605: Landroid/content/pm/PackageManager;.getPackageInstaller ()Landroid/content/pm/PackageInstaller;
D/dalvikvm: VFY: replacing opcode 0x6e at 0x000b
I/GMPM: App measurement is starting up, version: 8487
I/GMPM: To enable debug logging run: adb shell setprop log.tag.GMPM VERBOSE
E/GMPM: GoogleService failed to initialize, status: 10, Missing an expected resource: 'R.string.google_app_id' for initializing Google services.  Possible causes are missing google-services.json or com.google.gms.google-services gradle plugin.
E/GMPM: Scheduler not set. Not logging error/warn.
E/GMPM: Uploading is not possible. App measurement disabled
D/dalvikvm: GC_CONCURRENT freed 265K, 16% free 8722K/10356K, paused 5ms+2ms, total 26ms
W/dalvikvm: VFY: unable to find class referenced in signature (Lde/hof/my_project/enums/status/images/StatusImageScale;)
W/dalvikvm: VFY: unable to resolve static field 34720 ($SwitchMap$de$hof$my_project$enums$status$images$StatusImageScale) in Lde/hof/my_project/fragments/FragmentSplash$1;
D/dalvikvm: VFY: replacing opcode 0x62 at 0x0000
E/dalvikvm: Could not find class 'de.hof.my_project.tasks.images.TaskImagesScale', referenced from method de.hof.my_project.fragments.FragmentSplash.onViewCreated
W/dalvikvm: VFY: unable to resolve new-instance 9154 (Lde/hof/my_project/tasks/images/TaskImagesScale;) in Lde/hof/my_project/fragments/FragmentSplash;
D/dalvikvm: VFY: replacing opcode 0x22 at 0x0003
D/dalvikvm: DexOpt: unable to opt direct call 0xf89d at 0x05 in Lde/hof/my_project/fragments/FragmentSplash;.onViewCreated

Eu adicionei algumas saídas de log mor. É quando executo meu aplicativo em um Samsung Galaxy S3 com API 17 (minha API mínima exigida). Na semana passada, antes de atualizar minhas bibliotecas de 23.0 para 23.2, tudo estava funcionando. Agora parece que ele não consegue encontrar algumas das classes que defini.