Not sure how you end up ahead on a schedule if you stay on the plan?  So it's hard to answer without knowing your level.  Here are my last 3 weeks LR's before my last half I would say it's intermediate level:   4 out: 90 mins last 4 miles @ 1/2 pace and the last mile 10 sec faster then 1/2 pace. 3 out: 85 mins easy with 2 X 1 @ 1/2 pace. 2 out: 55 mins easy 3 X 800 @ 1/2 pace with 60 sec rest between. Or repeat your last three weeks.

I think it would beneficial to extend your LR schedule to at least 10 miles and adding the intervals, hill-work, cross-training and so forth might be of benefit.  Given the 10k time and the month left before the half, finishing around 2 hours would be difficult.  However, it depends on the course and many other factors in the coming weeks. 

I would recommend focusing on the LR and possibly splitting the mileage (a few days a week) if you have the opportunity, so running a route A.M. and P.M. (same day) to build endurance. 

The Coaches advice sounds like a great plan for you!  When I 1st started 1/2's I would only go to 10-12, I now go to around 15 and I do two hard days every week.    Good luck!

Splitting your runs allows you to get more miles in and helps you keep your form as you are doing less miles on tired legs, and is fine on any day other than your long run day.  You should run your long runs all at the same time!