Max,
Yes, you are correct.
A very large gap between coaxial rotors is most efficient for vertical lift due to the large effective disk area and low induced velocity per sq-ft. Conversely, the same rotors with a very small gap will have a smaller effective disk area and a higher induced velocity per sq-ft., and this would be better for forward thrust.
As you probably already know, this is the main problem with the tiltrotor (and the tiltwing) configuration, such as the V-22. It is using the same disk area for vertical lift as it is for forward propulsion. It must therefore compromise between the two requirements.
Sikorsky has a number of patents for a Variable Diameter Proprotors (larger diameter for hover and smaller diameter for propulsion) and this is aerodynamically attractive. However, the mechanism for obtaining variable blade span creates its own set of problems.
Your desire to place the counter-rotating proprotors in close proximity to each other, for propulsion during forward flight, is ideal since this will halve the disk area from when the are two aerodynamically separate proprotors and are providing lift.
It may (or may not) be impractical to get the coaxial proprotors in close proximity to each other for propulsion, as you are suggesting. My thinking is to allow a reasonable distance between the fore and aft proprotors, but have the diameter of the aft proprotor equal the diameter of the front proprotor's streamtube at the location of the rear proprotor.
This also should/may result in an 'effective disk area' that is the average of the actual front and rear disk areas. And just as with your idea, the effective disk area of the proprotors in forward flight will be half the disk area of the proprotors in hover.
The essence of this idea is probably the application of separate electric motors at each proprotor. Your idea will probably involve four identical motors, whereas my idea will require smaller motors on the aft proprotors and larger motors on the forward proprotors.
So far, so good.
Dave