Rod,
If I understand correctly what you have in mind …
I would probably not use a drawbar, but simply Loctite the collet adapter into/onto the drill shaft, using 638 [yes, I am a great advocate of the stuff
]
If you ever change your mind and want to revert to the original fitting, the Loctite can be softened at about 200°C or "destroyed" at somewhat higher temperature.
What's the present chuck fitting arrangement ?
MichaelG.