If you didn't want to use the hoops to pull it up on, consider a saddle strap undereath the car! When water skiiing you either have a single tow point on the boat say at the top of a wake board tower or in the centre of the transom. But if not then often you will see two eyelets one each side of the boat. A loop of rope (saddle strap) fixes to both these points and then the main ski tow rope attaches to this saddle strap via a small pulley block and can move side to side as you go around corners. This last feature is not what you need worry over for just pulling your car onto the trailer.as it is a straight pull. So if you look under the car in front of the rear wheel there maybe something there on the chassis where you can fix two small towing eyes to and then pull from under the car.
I had a boat trailer once with a folding arm at the front to the hitch. It was an American trailer and my research then said no folding hitch arms allowed in the UK. Annoying as it was a very good feature. Being an american trailer it had other issues that also prevented it being useable here. Shame as it was a great trailer. The rules may have changed in the last 15 years though!
If I were commissioning a trailer from scratch for my M3W personally I would go full floor as then the trailer could be used for multiple purposes. With the weight of the car so low I also would not be worried about using a single axle trailer. Often see those used for short lightweight cars. Not much of a wind side load on an open trailer compared to say a caravan. Easier to manouvre by hand too as only three contact points to the ground rather than five on a twin axle. And as you have alredy thought about, definitely get the nose weight on the hitch right as my brother jack knifed once decades ago with a car on the wrong way round. Wrote the tow car off in the process! Ooops!
I custom built a car trailer about 20 years ago, still use it today. I got the CoG of the car it was being built for and just as you are thinking, positioned the twin axles to suit whilst giving a good nose weight. Get it right and the trailer will simply fly along behind you with no snaking! Going back to boats for a moment, I think this is why all boat trailers seem to be various parts bolted together and not welded, so that they can be adjusted to suit whatever boat you end up buying. I have moved axles and tow hitches about to fine tune the towing experience.
A company called Peak Dynamics (used to be Peak Trailers) have a web site where you can look at all the parts ever needed to build your own trailer.
Sorry if I have rambled on a bit or gone off topic!
