Calculating tiles to display in a MapRect when "over-zoomed" beyond the overlay tile set

I am working on an app that uses MKOverlay views to layer my own custom maps on top of the Google base map. I have been using Apple's excellent TileMap sample code (from WWDC 2010) as a guide.

My problem - when "overzoomed" to a level of detail deeper than my generated tile set, the code displays nothing because there are no tiles available at the calculated Z level.

The behavior I want - when "overzoomed" the app should just keep magnifying the deepest level of tiles. It is a good user experience for the overlay to become blurrier - it is a very bad experience to have the overlay vanish.

Here is the code which returns the tiles to draw - I need to figure out how to modify this to cap the Z-depth without breaking the scaling of the frame being calculated for the overlay tile. Any thoughts???

- (NSArray *)tilesInMapRect:(MKMapRect)rect zoomScale:(MKZoomScale)scale
{
    NSInteger z = zoomScaleToZoomLevel(scale);

    // PROBLEM: I need to find a way to cap z at my maximum tile directory depth.

    // Number of tiles wide or high (but not wide * high)
    NSInteger tilesAtZ = pow(2, z);

    NSInteger minX = floor((MKMapRectGetMinX(rect) * scale) / TILE_SIZE);
    NSInteger maxX = floor((MKMapRectGetMaxX(rect) * scale) / TILE_SIZE);
    NSInteger minY = floor((MKMapRectGetMinY(rect) * scale) / TILE_SIZE);
    NSInteger maxY = floor((MKMapRectGetMaxY(rect) * scale) / TILE_SIZE);

    NSMutableArray *tiles = nil;

    for (NSInteger x = minX; x <= maxX; x++) {
        for (NSInteger y = minY; y <= maxY; y++) {
            // As in initWithTilePath, need to flip y index
            // to match the gdal2tiles.py convention.
            NSInteger flippedY = abs(y + 1 - tilesAtZ);

            NSString *tileKey = [[NSString alloc] 
                                  initWithFormat:@"%d/%d/%d", z, x, flippedY];
            if ([tilePaths containsObject:tileKey]) {
                if (!tiles) {
                    tile