I suspect that one or two folks have the lost the bit about this trip being in solid IMC.
I fly IFR/IMC in class G a fair bit around Southern England and there's a lot of complex controlled airspace, VOR/DME is generally accurate enough if it's on your route, but otherwise GPS is essential as far as I'm concerned.
I'd also avoid IMC flight without a radar service unless it wasn't available.
That said I've got two VOR/ILS a DME and a ADF and I'll have 'em all tuned idented and selected if they're available as well as a chart on my lap. I see no harm in having belt, braces and a piece of string to hold up one's trousers in IMC.