I'm going to sneak in here to clear up some of the reg type questions brought up.
was wondering about the regulatory position regarding DME being a requirement for IFR
Per 91.205 (e)
(e) Flight at and above 24,000 feet MSL (FL 240). If VOR navigation equipment is required under paragraph (d)(2) of this section, no person may operate a U.S.-registered civil aircraft within the 50 states and the District of Columbia at or above FL 240 unless that aircraft is equipped with approved DME or a suitable RNAV system. When the DME or RNAV system required by this paragraph fails at and above FL 240, the pilot in command of the aircraft must notify ATC immediately, and then may continue operations at and above FL 240 to the next airport of intended landing where repairs or replacement of the equipment can be made.
So you only need DME (or GPS) at or above FL240.
can't see any alternative means of establishing this fix other than by DME. Must have missed something horribly obvious
No regulation on this but AIM 5-3-6 tells us:
Pilots are urged to observe COPs to the fullest extent.
Obviously without DME this will be tricky, but a time based estimate would be acceptable in this case. Or the more intuitive "huh I'm not getting that VOR anymore, time to switch to the next one". It isn't the end of the world if you are off by a couple of miles, the tolerances are never that tight (except where there is a turn involved in which case the cross radial is your exact guide).