Recently had similar experience to you th0rpey0 and was all set to get an Airshot but hesitated and called the bike shop instead to see of I could borrow their compressor.
They said Ok, but when I turned up the compressor was out of action, so they tried their own Airshot, without success.
The guys finally got the tyres to seat with a CO2 cannister per wheel.
Before investing in an Airshot, give the CO2 method a go. It only costs a couple of quid.
The technique they used was a bit different in that they put some latex in first, then put the rim on the wheel and then let rip with the CO2.
The cold can have a negative affect on the latex apparently, and I guess if the tyre fails to seat, there’ll be a latex eruption as the gas goes in… …and out, so it is not exactly textbook.
But it could save you £60!