You can write you own custom control (based on Canvas, Panel, etc...) and override OnRender, like this:

   public class BigGrid : Canvas
    {
        private const int size = 3; // do something less hardcoded

        public BigGrid()
        {
        }

        protected override void OnRender(DrawingContext dc)
        {
            Pen pen = new Pen(Brushes.Black, 0.1);

            // vertical lines
            double pos = 0;
            int count = 0;
            do
            {
                dc.DrawLine(pen, new Point(pos, 0), new Point(pos, DesiredSize.Height));
                pos += size;
                count++;
            }
            while (pos < DesiredSize.Width);

            string title = count.ToString();

            // horizontal lines
            pos = 0;
            count = 0;
            do
            {
                dc.DrawLine(pen, new Point(0, pos), new Point(DesiredSize.Width, pos));
                pos += size;
                count++;
            }
            while (pos < DesiredSize.Height);

            // display the grid size (debug mode only!)
            title += "x" + count;
            dc.DrawText(new FormattedText(title, CultureInfo.InvariantCulture, FlowDirection.LeftToRight, new Typeface("Arial"), 20, Brushes.White), new Point(0, 0));
        }

        protected override Size MeasureOverride(Size availableSize)
        {
            return availableSize;
        }
    }

I can successfully draw and resize a 400x400 grid with this on y laptop (not a competition machine...).

There are more fancy and better ways of doing this (using StreamGeometry on the DrawingContext), but this is at least a good test workbench.

Of course, you'll have to override the HitTestXXX methods.