GPS is a problem. From browsing through the official strategy document (for Norway), there are two main issues for civilian aviation.
The solution is to keep traditional navigation systems as fully functional “backup” as long as they last and it’s an economical option. By the looks of it (from Avinor visual approach carts) this results in more DMEs and less NDBs and VORs.
The main direction is still GPS though. But there are other stuff going on also. Last year Avinor finished their network with over 200 WAM stations. It’s normal operational mode is with GPS (standalone or with ADS-B), but it will also operate without any GPS. WAM needs very precise timing, which is cheap and easy to get with GPS. Without GPS, atomic clocks are needed, which is being installed now. WAM/ADS-B is not a navigational system, but with ADS-B-in it certainly could be used as such for GA also without GPS. As a GA pilot today, with an old mode C transponder, I’m only a radio call away to know my exact position, even without radar or GPS.
However, googling this stuff I found another slightly disconcerting thing. In Norway there has never been any focus on mode-S. For GA transponder is optional, but mode C is required in controlled airspace wherever/whenever ATC say it is. The aviation authorities together with Avinor and the met office has plans to make ADS-B mandatory in all controlled airspace from 2030 already. The disconcerting part is that the GA community as a whole would welcome this, due to all the upsides as online weather and a standard traffic information system system for everyone (not the jungle it is today). This will also include drones. There will be close to zero opposition to it, and therefore it will be implemented.
Any future DME would have to offer more than simple distance to a station. In an ideal world it would be a unit capable of simultaneously accessing two or more DME stations, to make this a flexible navigation system the unit would require a database.
It follows that the DME should be able to access the GPS database and present position data using the equipment currently presenting the GPS information. This will not be a panel mount unit but one that will be remote mounted and controlled via software presented on the GPS or the ND. It would also have a lock function for use during approach .
It would be my guess that the reason we have yet to see a DME from Garmin is the KN 62/63/64 range (& KR87 ADF ) had been developed by Gary Burrell before he left King avionics to set up Garmin and he saw little advantage in duplicating what is a very reliable unit…… so he just made sure that Garmin Avionics were compatible with the King DME & ADF.
As GPS jamming and spoofing are now real dangers the market needs a reliable alternative navigation system be that DME or eLORAN.
Peter wrote:
In fact you need only 1 DME to get position!How does that work?
How does that work if you fly an arc around the DME?
Even if you are tracking a single DME beacon, the solutions are constrained by your heading (from the fluxgate magnetometer), your TAS (you have IAS + OAT + pressure altitude) and obviously where you think you have just been.
In reality any implementation has a database of DMEs and it tunes them as it moves along. This is necessary as they move out of range. The tuning of a DME box is instant, so you need only one. And if you are tuning the DME, you may as well use any beacon that’s in range.
The problem, as always, is that the volumes are low, and GPS is extremely reliable and precise, so few people are bothered. And there are solutions involving FOG INS combined with GPS – exactly what is done in missiles etc.
Peter wrote:
The clue is in “multiple simultaneous equations”
AKA rocket science 
INS is amazing stuff. A gimbaled INS can align itself when stationary, you only have to enter the longitude. When moving in a straight line, I would think the velocity component in N-S is always known from the INS without any alignment. You will always be able to move straight E-W. Don’t know how the math becomes (except terrible), but an INS is an analogue computer that solves lots of equations all by itself. But the errors adds up over time, and it needs to be initialized and corrected.
The clue is in “multiple simultaneous equations”
How does that work?
You’re not going to get away with that. How is it done? Doppler?
In fact you need only 1 DME to get position!
How does that work?
Ask someone who does satellite launches 
It has been a standard technique since the 1960s. You end up with 100s or 1000s of simultaneous equations and you solve them continuously. The solution is constrained by various factors; in our case it is aircraft performance and in the satellite case it is that plus orbital mechanics. You do need to initialise the system appropriately.
I was told by a Concorde pilot in 2003 (I was on one of the last flights) that they use a single DME for their INS corrections. I already knew of the single DME method so I didn’t question him (also everything was rushed) and prob99 he would not have known the mathematics involved. But he did specifically say it was 1 × DME because I mentioned the standard 2x DME method. It does take a fair bit of computation which in the 1960s was a fair bit of hardware, whereas today a $3 ARM32 chip can easily do.
For the DIY DME, a source of inspiration could be the Mode C DIY tranponder posted here: https://www.euroga.org/forums/maintenance-avionics/6851-build-your-own-avionics/post/124813#124813
A receiver could be designed to use the ADS-B UAT ground stations and determine position. The UAT frames are synced to the same time reference. In the US, there a more than 650 ADS-B ground stations. Europe could get on the band wagon and use UAT ground stations also to send FISB products to aircraft, so it would serve two purposes.
