Yeah, I was going for keeping the trail lengths most even, and then worrying about preferences secondarily. Satisfying the preferences makes the distance spreads very large, as in Richard Pearse’s post. The OP needs to decide which is more important.
This is looking more and more like a case of too many variables for a definitive answer!
Yes, some distance spread is to be expected. It just seems like our current assignments are out of whack because we have our second-slowest runner (JF) doing the second-longest distance (and time), and our fastest runner (AT) doing the third longest distance and the third shortest time.
The math nerd in me wants to fix that. But the social pleaser realizes that if everyone seems to be happy with what we’ve got right now, who cares if we come in 20 minutes later?
So here is my suggestion. I believe it fulfills everyone’s desires except JF only gets one leg instead of 2 separate legs, because only JF and LA are willing to run on trails. LA consequently is shouldered with a heavy load of two large legs. I gave AT legs 6 & 7 because that was requested, resulting in an above-median length. Everyone besides LA & AT has run times of an hour and a half, give or take 10 minutes.
Leg 1: 4.8 mi: AS @ 11.5 min/mi = 55’12"
Leg 2: 4.6 mi: KS @ 10.5 min/mi = 48’18"
Leg 3: 6.5 mi: AM @ 14.0 min/mi = 91’
Leg 4: 4.0 mi: KS @ 10.5 min/mi = 42’
Leg 5: 3.4 mi: AS @ 11.5 min/mi = 29’ 6"
Leg 6: 7.8 mi: AT @ 10.0 min/mi = 78’
Leg 7: 3.0 mi: AT @ 10.0 min/mi = 30’
Leg 8: 7.7 mi: LA @ 11.5 min/mi = 88’33"
Leg 9: 7.7 mi: JF @ 13.0 min/mi = 100’ 6"
Leg 10: 5.8 mi: LA @ 11.5 min/mi = 66’42"
Runtimes:
AM: 91’
JF: 100’ 6"
AS: 84’29"
LA: 155’15"
KS: 90’18"
AT: 108’
Total time: 10 hours, 29 minutes, 8 seconds
OK, wow, that it interesting because it’s very close to what we (the team) were working from, yet it shaves off 20 minutes:
TEAM:
Leg 1. 4.8 miles AS
Leg 2. 4.6 miles KS
Leg 3. 6.5 miles AT
Leg 4. 4.0 miles JF
Leg 5. 3.4 miles AS
Leg 6. 7.8 miles AM
Leg 7. 3.0 miles AT
Leg 8. 7.7 miles LA
Leg 9. 7.7 miles KS
Leg 10. 5.8 miles JF
Punoqllads:
Leg 1: 4.8 mi: AS @ 11.5 min/mi = 55’12"
Leg 2: 4.6 mi: KS @ 10.5 min/mi = 48’18"
Leg 3: 6.5 mi: AM @ 14.0 min/mi = 91’
Leg 4: 4.0 mi: KS @ 10.5 min/mi = 42’
Leg 5: 3.4 mi: AS @ 11.5 min/mi = 29’ 6"
Leg 6: 7.8 mi: AT @ 10.0 min/mi = 78’
Leg 7: 3.0 mi: AT @ 10.0 min/mi = 30’
Leg 8: 7.7 mi: LA @ 11.5 min/mi = 88’33"
Leg 9: 7.7 mi: JF @ 13.0 min/mi = 100’ 6"
Leg 10: 5.8 mi: LA @ 11.5 min/mi = 66’42"
I like that it gets KS off the trail portion and shortens AM’s distance, but not embarrassingly so. Pretty sure LA would be OK with the longer distance; she’s an animal (and it’s split up, so not so bad). AT gets her leg preferences and a decent distance. I’ll have to see what JF thinks.
Are you psychic? 
And I (AS) could swap Leg 8 with LA (so I don’t end up running at both start and finish) and thus transfer one of her miles to my total. As I added later in the thread, I won’t mind running trail if necessary, I just prefer not to if possible.
This is wrong, should be 39’ 6". So add 10 minutes to AS’s time and overall time. Half the shave, alas.