Hi Dave,
If you can find an instructor who is willing, you can do your training in the LongEz, though I have to say that I think instrument training is easier done with the instructor sitting beside you, for a couple of reasons.
The first is that much of instrument flying is about precisely controlling the airplane - pitch, yaw, roll, airspeed, and altitude. I believe most instructors would want/need to be able to see all of the flight instruments. I believe that you would want them to be able to see them also. It helps him (her?) point out things that you might be missing. If you would like to be able to get some actual IMC experience (which I recommend), I can't imagine an instructor riding in the back while IMC without having a full panel to look at. Maybe your plane has the full complement for GIB?
I also wonder how your instructor would setup unusual attitude exercises without access to all of the flight controls, to include throttle, trim, and rudder. Especially as a model for having a hosed AP, having the instructor mess with the trim wheel is a good exercise.
Another issue to contend with is dealing with all of the paperwork in the cockpit. If every flight goes according to plan, the paperwork is pretty easy. If your instructor, the plane, ATC, or weather starts throwing you curve balls, just doing the chartfolding in the tandem cockpit could be a chore.
Now, the other side of the coin is that the LongEZ has good stability, with excellent, high altitude performance, comfort, endurance, and range. This is a HUGE benefit for actually using the plane as an IFR platform, and for doing x-country work. Lots of margin when considering alternates. The high-ish wingloading, and strong dihedral effect means that the airplane handles well in turbulence. I'd put a LongEZ against an RV4 any day, as far as hands-free flying. I have done most of my IFR training in my C150. It's okay, but it lacks range-endurance, comfort, high altitude performance, and it bounces like a cork.
Would you intend to checkride in the LongEZ? That may prove to be a challenge as well, for most of the reasons above. Have to find a DE that would ride in the back..
Finally, you asked about ADF/DME. For the checkride, you'll have to demonstrate precision and non-precision approaches. The VOR/GS allows this, so no problem there. The issue I see is that you will get very bored flying just those two types of approaches. If you're anything like me, I could fly the basic VOR/GS approaches to PTS standards after about 5 hours under the hood. Having more equipment means you can learn more approaches, which is useful and fun.
My airplane has an ADF, but no GPS or DME... Using a non-approach GPS to learn other types of approaches can be effective, but I think you miss out on some of the useful things to be learned by having the actual box in the airplane. For instance, ADFs wander, and have limited range. Identifying the station letters everytime you fly the approach is an important habit to develop. Wind correction can sometimes be a challenge with the ADF. I have faked it with a handheld GPS to fly DME required approaches, and used the handheld to assist in situational awareness on NDB approaches. The handheld almost makes it too easy..
There may be times when you want to be able to fly IFR in an airplane which doesn't have a GPS. So, you can do what you are suggesting, but I think you are short-changing yourself in the end.
Good luck!
Matt-
