Interesting. My reasoning would've been completely different, but leads to roughly the same answer. I would have thought that if you want a half-hourly service, then you need to place the loop somewhere that allows reasonable dwell times at Blackpool South. Say 10 minutes, which gives a few minutes recovery time for late trains. (No point giving more than a few minutes recovery time because the nature of single track working means the timetable is completely screwed anyway if a train is more than a few minutes late).
That suggests that you want the loop and therefore the train passing-place to be just under 10 minutes from Blackpool South, so that a train is in the right spot to pass the train half an hour ahead/behind it. St. Annes is 8 minutes from Blackpool South, so that seems to be the best location: 16 mins to/from Blackpool South, and say 2 mins for a train to get from having passed the previous train at the station to get out of the loop, giving 12 minutes dwell time at Blackpool South. Lytham isn't remotely a good location by that reasoning, unless you can reduce journey times substantially.
Don't understand the relevance of equalising the time to reach Kirkham, unless you specifically want the trains to pass exactly at Kirkham (and not anywhere else East of Kirkham)
