The only other alternative I can see without changing existing taps or paying for expensive extensions, is to plug your existing holes and start from scratch drilling the counterbore first then re-drilling the plug out. Before inserting the plug I would drill a small pilot hole down the centre, this will assist in keeping your flat/Forstner bits on centre. I should imagine you only need to counterbore about 20mm deep to accommodate most back nuts and tap connectors I have experienced.

Richard