The running time from Windermere to the Airport appears to be 2 hours and 4 minutes, inconveniently.
You can do Oxenholme-Windermere-Oxenholme as a shuttle in an hour with layovers. So if you add that on, each "cycle" (Airport-Windermere-Oxenholme-Windermere-Airport) would be 5 hours and 8 minutes. Slightly inconvenient, but if you take that to 6 hours that's probably a sensible layover of 52 minutes in the whole cycle to cover the long distance round trip. Not sure if the Airport could accommodate this for a 4-car unit? If not, it could perhaps operate all stations on the Airport line to slow it down a bit?
6 hours is quite a nice length for the cycle, as that could do a 2 hourly long distance service plus a shuttle in between using the 3 units ordered. Spares could come from the Class 195 pool, i.e. if the EMU isn't available, just use a pair of 2-car DMUs, or if there's a real shortage that day put a spare EMU on, run it to Oxenholme only and put a bus on for the last bit.
Not running Barrow quite as frequently would also free up a couple of 195s for other uses. I'm pretty sure in the 90s it was more or less alternated, it's TPE's tenure that cut it right back and turned the fairly neat NorthWest Express timetable into the present inconsistent mess.