Hello mate
Theres not that much more you can do really in terms of adjusting your weight training as that is a very consise training program as it is. The obvious advice would have been to stick to core lifts, few sets and low reps to try and maintain as much strength as possible, but you already do that.
Perhaps drop down to 2 days a week of lifting , maybe one ? You aren't going to get any improvement in your lifts whilst simultaneously doing long distance running so my opinion is that you might as well do only enough lifting to try and limit the damage of the running on your strength and keep an eye on recovery.
Look at your diet as well, it may be neccessary to adjust carbs and protein (up) to cope with the extra activity and try and spare your muscle. If possible get some advice on how the shape of your body and posture ( which will be affected by the muscle being carried, and disproportion caused by lifting ) can be improved to avoid injury. Lifters and ex lifters tend to run hunched over, and in my case lop sided from old squat injuries.
Take a look at interval training, the format of it will appeal to a weight lifter, its quick and hard and structured a little like sets and reps that you will be accustomed to.
Sorry for waffling. Good luck, it'll be bloody hard. And if you are doing 4 miles within a week then you made the transition a hell of alot better than me
