my berlingo was fine going through as a car, I know the expert is a bit larger but give them a call. I think it's more about height/which deck you can put it on rather than if it's a commercial vehicle (windows etc).
I've got the L2H1 version, but it's the Tepee model with window all round. I often cross, a dozen times a year, using the tunnel often loaded up with junk, furniture, logs etc and with the back seats removed and always go through as a standard car. I haven't had any questions asked yet, I book as "car with roof rack" as it's too high to go in the double level trains. I know some ferry companies charge extra for length so it's worth checking carefully.
I booked my Astra van in as an Astra estate.
I booked over the phone to be sure and told them what I had done, no probs they just want the business. Also told them it was a private journey/ holiday, no goods in transit.
Like others we had no issues with taking our van over in the tunnel last summer as a domestic vehicle. Vito van with no side windows back seats or conversion to camper. As others said had to be loaded into a double height section but the price was (I think) the same as if we had taken a car over.
Always thought it's based solely on height and length? Been several times in a transit, always just booked on as a private vehicle.
Went by Chunnel once, filled in the form accurately and it said my SWB Low Roof Transit was car dimensions so booked a car ticket. Argued for a while at check in, got them to measure it, and it came in (as I knew it would!) under the car length and height sizes. Result!