Philip, if you're still running the twice short once long you have listed in your post from July, I don't think your plan is likely to get you faster without injury. Your problem isn't speed - you just ran 1.5 miles faster than your goal pace. Your problem is endurance - stretching out that faster running to encompass four times as many miles. Concentrating on speed is missing the point, and more likely to injure you than concentrating on overall weekly mileage and endurance.

If you could run more frequently, and make your short runs longer, I think that would support occasional tempo runs. You also might consider throwing strides into your easy runs: accelerate for a slow 6-count to the fastest pace you can hold with good form, hold it for another slow 6-count, then slow to your usual pace over 4-6 more seconds. Recover fully from each stride before doing another, and do 2-5 of them.

If you could turn two of your weekly short walks (60 min) into long runs (gradually! Maybe combining them at first, walking for 45 minutes and running 15, e.g.), thus running 5 times a week for 3:44 total, I think that would do more to help bring your running speed up than anything else. And it would not change your total time commitment to exercise. I also think that, if you ramp up slowly and easily, and keep your pace for most of your runs easy, this will actually reduce your likelihood of injury.

Good luck!