As far as the DME is concerned, I think the argument is that it does not measure slant range and therefore does not tick the box in the same list as above.
I think (really knowing nothing of legal practicalities) that any courtroom argument supporting the carriage of a GPS without a DME would not spend too much time on the slant range issue, which is an utterly insignificant error in most cases.
I think the "distance measuring equipment" wording would be met by a GPS.
But who knows? It's never been legally tested, TMK.
You might get a problem with insurance paying out following a prang, off an IFR flight planned flight, not carrying the specified equipment. Aviation insurance does pay out readily but not where the flight was illegal before it left the ground. I have discussed this with a loss adjuster and that (not being illegal before departure) was important.
Re the Cirrus installation, this is partly why in 2001/2002 I decided to not give £200k+ to the arrogant ******** manning the Cirrus stand at N Weald (or was it Booker?) when I asked about fitting ADF+DME and he told me that a GPS is better than an ADF and then turned around to talk to another punter who was presumably not asking as many Qs. If this was his pre-sales attitude, what of the post-sales attitude?? Cirrus UK knew from day 1 they were illegal and their customers would have to sort it out themselves someday.
I gather than on glass versions there are remote reading options. On the steam gauge version, a RHS mounted KR87 and a DME of some sort (KN63 is a nice little one which might fit in the LHS).
Personally, I would not fly without a DME, because VOR/DME is a highly desirable backup for a GPS and I've had to use it too (just once, though I did have other GPS options). Enroute, I always have VOR+DME tuned.
The ADF argument is more tricky. If I had one (which I do; KR87 which is the only reliable GA ADF on the market) I would not chuck it out. I had a KI-229 dual-needle RMI fitted which combines a VOR (switchable NAV1/NAV2) and ADF indications and this is an efficient way of putting in an ADF - you don't waste indicators because an RMI is brill for all kinds of VOR stuff including flying arcs around a VOR/DME. But I admit this is 1990s avionics really.