Why did they chart the non-DME minimums if one of the two DMEs is likely to be in service?
It's based on primary NAV aid philosophy in case of VOR 18 primary NAV AID is LIN with the associated DME. ILNT DME is supplemental only. The minima is based on usage of primary NAV AID.
And, essentially the OP's question, how do you safely fly to the non-DME minimums (1050 MDA) without either DME?
This NON DME or VOR min is based on LIN DME OUT condition ONLY. Even though one will be able to identify all the waypoints by using ILNT DME the applicable minima in case of LIN DME OUT is 1050. Alas, the question of plausibility is irrelevant. To answer your question: it's not possible to fly VOR 18 in case both DME out. The only reason why the briefing strip doesn't say LIN DME required is due to the availability of backup ILNT therefore providing sufficient redundancy. That's also a reason why VOR 36 says LIN DME required and therefore no DME OUT mins are available. IOW you cant fly VOR 36 in case of DME OUT. Hope that makes somewhat sense. However the whole approach to construction of this kinda approaches only proves impracticability of European mindset, I'm afraid.
