I misunderstood slightly. However, I'm not sure your conclusion works. For instance this TPE service:
http://www.realtimetrains.co.uk/train/Y01770/2015/05/18/advanced is shown as being pathed for a 75mph DMU but doesn't appear on your list. Yet TPE did say they would run 3 diagrams using 156s in 4 car formations mainly on Blackpool services.
I *think* I've worked it out. The 08:31 Manchester Oxford Road - Barrow drops the rear 156 at Preston, and the 13:40 Blackpool North-Manchester Airport joins a 156 at Preston. (There are ECS movements to and from Lancaster.) However, they don't seem to be the same 156! It seems that the one that detaches goes off onto Northern services on the Cumbrian Coast, and then comes back the next day.
This, then, is my best guess at the TPE 156 diagrams from May onwards, with thanks to samj for his first attempt:
Diagram 1
5U54 (ECS) 06:55 Blackpool North CMD - Blackpool North 07:00 (with diagram 2)
1U54 07:17 Blackpool North - Manchester Oxford Road 08:27 (with diagram 2)
1C51 08:31 Manchester Oxford Road - Barrow-in-Furness 10:52 (with diagram 2 to Preston)
1N13 11:13 Barrow-in-Furness - Blackpool North 13:09
1U67 13:40 Blackpool North - Manchester Airport 15:15 (with diagram 3 from Preston)
1N65 15:29 Manchester Airport - Blackpool North 17:06 (with diagram 3)
1U74 17:20 Blackpool North - Manchester Airport 18:51 (with diagram 3)
1N71 19:29 Manchester Airport - Blackpool North 21:05 (with diagram 3)
1U84 21:34 Blackpool North - Manchester Airport 23:16 (with diagram 3)
1N30 23:30 Manchester Airport - Blackpool North 01:00 (with diagram 3)
5N30 (ECS) 01:10 Blackpool North - Blackpool North CMD 01:15 (with diagram 3)
Diagram 2
5U54 (ECS) 06:55 Blackpool North CMD - Blackpool North 07:00 (with diagram 1)
1U54 07:17 Blackpool North - Manchester Oxford Road 08:27 (with diagram 1)
1C51 08:31 Manchester Oxford Road - Preston 09:22 (with diagram 1)
5C52 (ECS) 09:32 Preston - Lancaster 11:23*
1C52 12:01 Lancaster - Barrow-in-Furness 13:06
1N32 13:10 Barrow-in-Furness - Lancaster 14:04
-- transfers from TPE to Northern --
2C79 14:24 Lancaster - Morecambe 14:35
2C70 14:38 Morecambe - Lancaster 14:49
2C43 15:33 Lancaster - Carlisle 19:10
2C46 19:15 Carlisle - Whitehaven 20:25
2C37 20:30 Whitehaven - Carlisle 21:39
2C34 22:00 Carlisle - Whitehaven 23:10
5C34 (ECS) 23:14 Whitehaven - Workington HS 23:42
Diagram 3
5C32 (ECS) 05:41 Workington HS to Maryport 05:55
2C32 05:59 Maryport - Preston 09:30
2C73 11:08 Preston - Morecambe 11:40
2C74 11:45 Morecambe - Lancaster 11:56
2C75 12:04 Lancaster - Morecambe 12:14
2C76 12:38 Morecambe - Lancaster 12:49
-- transfers from Northern to TPE --
5U67 13:20 Lancaster - Preston 14:05
1U67 14:05 Preston - Manchester Airport 15:15 (with diagram 1)
1N65 15:29 Manchester Airport - Blackpool North 17:06 (with diagram 1)
1U74 17:20 Blackpool North - Manchester Airport 18:51 (with diagram 1)
1N71 19:29 Manchester Airport - Blackpool North 21:03 (with diagram 1)
1U84 21:34 Blackpool North - Manchester Airport 23:16 (with diagram 1)
1N30 23:30 Manchester Airport - Blackpool North 01:00 (with diagram 1)
5N30 (ECS) 01:10 Blackpool North - Blackpool North CMD 01:15 (with diagram 1)
Diagram 4+5
5U53 (ECS) 06:19 Blackpool North CMD - Blackpool North 06:24
1U53 06:35 Blackpool North - Manchester Airport 08:17
1N56 08:25 Manchester Airport - Blackpool North 10:03
1U61 10:40 Blackpool North - Manchester Airport 12:15
1N62 12:29 Manchester Airport - Blackpool North 14:04
1U69 14:36 Blackpool North - Manchester Airport 16:21
1N66 16:29 Manchester Airport - Blackpool North 18:05
1U77 18:43 Blackpool North - Manchester Airport 20:23
1N72 20:29 Manchester Airport - Blackpool North 22:03
1U86 22:45 Blackpool North - Manchester Airport 00:26
5K86 (ECS) 00:27 Manchester Airport - Manchester Piccadilly 00:43
Diagram 6+7
5N63 (ECS) 05:53 Manchester Piccadilly - Manchester Airport 06:07
1N53 06:18 Manchester Airport - Blackpool North 07:56
1U57 08:40 Blackpool North - Manchester Airport 10:17
1N59 10:29 Manchester Airport - Blackpool North 12:09
1U65 12:40 Blackpool North - Manchester Airport 14:15
1N64 14:29 Manchester Airport - Blackpool North 16:09
1U73 16:36 Blackpool North - Manchester Airport 18:17
1N69 18:29 Manchester Airport - Blackpool North 20:07
1U81 20:42 Blackpool North - Manchester Airport 22:18
1N76 22:29 Manchester Airport - Blackpool North 00:04
5U76 (ECS) 00:09 Blackpool North - Blackpool North CMD 00:14
* Note that for some bizarre reason 5C52 sits in Barton & Broughton loop from 09:40 to 11:05!
This is 7 diagrams rather than 6, but half of each of diagrams 2 and 3 are Northern, so I think it's plausible... I may, of course, be completely wrong...