Very deep hole saw needed

[indecon]

I need to drill an 86mm dia hole through a 4 inch thick timber frame. Hole saws seem to max out at 50mm deep. How can I produce a clean hole? I could get to the other side (double brickwork) but I would need an SDS+ arbour about 8 inches long to get to the other side of the wood. Does anyone know where I could get a 86mm dia hole saw about 100mm deep?

 

[Symptoms]

con - do it in stages to the max depth of the hole saw, extract the saw, chisel out the lump, insert the saw, cut the next 'layer', extract the saw, on so on 'til you're through.