Niall's suggestion is worthy of consideration and I expect the locals are having the same thoughts. The road is rarely that busy but crossing the street is not ideal and this is a time to at least consider the option.
It strikes me that a new clubhouse could be built on the opening hole of the 9-hole course and still maintain 18 as the closer. This would entail a long march to the 1st tee, but it's nothing they are not used to when playing the 9-holer or using the practice area. One can also imagine golfers would leave their trolleys back down the fairway and stride up with just driver (and a spare ball in hand). It would be quite the talking point to take the walk with just the one ball! I expect this location would incur the wrath of the homeowners along the main road, because it destroys their clean view across the links and for that reason alone it may be discounted.
Building a new CH up towards the 17th green would involve a lot more work on an entrance drive and would bisect the flow of the 9-hole course, but would give them more options with regard to the layout of the buildings. The added distance from the road may less offend the neighbours too. Quite a lot of work to reroute the 9-holer but nothing too arduous.
As to saying the 1st would become only 10% of the hole it is just because it is changed to the 2nd is frankly a bit daft and devaluing to the argument behind the claim, because the statistic has no credibility. Ballybunion moved their clubhouse from one end of the links to the other and it was fine. Walton Heath will do the same when they relocate and it will be fine too. Woburn was designed around a clubhouse in a completely different spot and that seems to have worked out OK. The Mach members have an enforced opportunity to look at the bigger picture and only they can decide if the iconic stature of the 1st hole as a 1st hole is a dealbreaker. If it is, then the options are limited...and that is fine too.
I'm sorry for them all to be facing this trauma, but hopefully they are adequately insured and will, in time, emerge with a superior building and facilities. As Sean said, it wasn't the greatest of houses.