Single track running at 3mph....ha..ha!
I know it's tempting to imagine some old preserved funicular tram trundling up and down the Great Orme as a tourist attraction, but modern funiculars are actually pretty good. My wife's family lives quite near the Carmelit railway in Haifa and the cars are Swiss built, and feel well-engineered and comfortable, if aging somewhat. The line can travel its 1.1 mile length in about seven to eight minutes with multiple stops; with no stops it would be much faster. I never felt it was slower than any "normal" light rail system.
I think the biggest problem for the funicular suggestion might perversely be a
lack of a sufficient gradient - which will need to be fairly steep.
On that premise there is nothing stopping the airport bringing the link in house again and providing their own bendy bus service. Now whether they would want to do that and absorb the cost when they charge for everything else including plastic bags is another matter but then that brings back the question if they provide a dedicated link at say a cost of £100 million would they then want to run it for free. If they didn't then there is the same set of passengers that is queuing today to pay the fare for a bus that would queue to pay for some sort of rail link so where is the integartion and seamless travel? The link will only improve if passengers just get on it and then go without dipping their hands in their pockets.
If the airport management are interested in bringing it in-house there are currently a bunch of ex-London Mercedes Citaro bendy buses in reasonable condition going on eBay for around £10k each.
I know you should never buy ex-London but these were withdrawn well before the end of their useful service life. They might last another ten years.
Anyway, the bodge of an answer is to rename Luton Airport Parkway to something anonymous like "Luton South" so that everyone in future buys tickets to "Luton Airport". Better, I don't know what issues may be involved here, but Luton Airport could become part of the rail network and appear on rail maps as a spur, and as a rail destination in its own right - even if the physical track doesn't actually exist and is actually served by a "permanent replacement bus" service.