Keep It Simple Stupid!!
The fact that you can't do a GPS/DME arrival "for whatever reason" suggests the aircraft and/or ground equipment is u/s or not fitted...surely unlikely in this day and age!!
That being the case common sense suggests you will be unable to determine accurately where 3nm is...making the VFR alternative unattractive, impractical and possibly illegal. Although I would agree with the premise that there is nothing illegal about useing VFR procedures on an IFR flight...just not in this scenario.
So the simplest solution is to maintain LSALT or MSA until overhead and descend to circuit ht upwind/crosswind before flying a perfectly normal circuit and landing. As you suggest the obstacle allows normal circuit ht and will be out of the picture by the time you leave circuit alt on base.
Dark hole approaches sans vasis/papi are fraught with peril...there is simply no reason to complicate a dangerous situation to save 3 minutes...it's called airmanship!!!
Chuck.