I own 4 CT's, 2 in the house/shop, 2 in the field. All have been modified. I won't describe how to do it, but I'll tell you why.
I don't know why the supplied cords are configured the way they are, and I don't really care. They don't work for me.
The first time on a job with my first CT, I lost the adapter plug. Right then and there I performed a "field modification" to get me through the day. I also found that the good quality heavy black cord originally installed on the vac behaved like an angry python when I tried wrangling it back into it's cage at the end of the day. Too much effort just to get home!
I have since shortened all of the vac's cords to about 12'" ( or direct wired in the case of the shop vac) to be used with extension cords that fit the requirements of the job conditions. Yes, I can't plug directly into a wall outlet, but I'm glad to be without the adapters and unwieldy factory cords.
Dan