"so what's the best way to add in a proper strength training routine?"
http://www.furman.edu/sites/first/Documents/16_oct2324.pdf

For your consideration.

i can never calorie restrict when i'm training for a half, because otherwise i am rungry All The Time. i find that on long run days, my net calories are way lower than goal, but the next two days after that i want to eat everything in sight. those are the days i have to work really hard to maintain.

I run 5x a week, XT once, and do strength training 2x a week. I was doing Body Pump when preparing for both my HMs. I like it because it's more about high reps / low weight. When training for my marathon, I stopped when I had Runner's Knee. Now, my son has soccer schedule conflicts with class times so I'm working on creating my own weight training program that is a combination of barbell weights, dumbells, core, some body weight exercoses and plyometrics that are supposed to be beneficial to runners. I've only done it once so far, but I'm scheduled to do it again today.

You don't have much to lose to get to your goal weight. I went on vacation early August last year, gained about 8 lbs over goal weight, lost a few, then went to Afghanistan for 2.5 weeks where food is the highlight of the day. Lol! I still ran over there, but I walked A LOT more than normal too. I came back 5 lbs over goal weight in mid September and was able to lose it by my 1st half on October 1st. It's hard, but I wanted to be at my prime weight. I finished in a little over 1:48:00 and won 2nd in my AG.

I guess I'm trying to say it's possible to train and eat in a small deficit, but it's hard and took a lot of will power. On the other hand, the amount of weight you are over goal weight isn't going to have a major impact so if you just want to maintain until after the race, that's fine too. The thing is that if you still plan to do long runs after your half, you're still going to have the rungry issue.

I'll start off with weight loss while endurance training. The simple explanation, not a good idea because you are typically going to be burning more muscle being at a caloric deficit. There are plenty of articles you can search for on the details of this if you like. However, if you really want to lose weight during, you need to be really focused on your nutrition. This typically means a lot more protein. This will also help you combat your runger.

Next, you need to add strength training to this. Yes, many runners don't strength train and end up just fine. However, most runners need to strength train. It promotes so many good things, there are too many to list; aiding in injury prevention, improved speed, improved performance, just to name some biggies. However, you don't need to be a body builder. Just get in at last 2 full body sessions...preferably 3, but 2 should be minimum.

Finally, your run schedule is minimal but definitely fine, as long as the 2 non-long runs are high intensity. You will see the most benefit from quality over quantity. Tried and true minimal is Sprint/Intervals, Tempo, Long. Looks like you probably are doing that.

As a final note, usually to combat runger for myself, I have a protein shake after my runs...I am pretty hooked on Quest protein...soooo tasty. I do this for marathon and triathlon training as well.

I avoid runger by increasing fat, as well as the protein previously mentioned, and ensuring to re-hydrate after a run.

For strength I do Stronglifts 5x5 2 days a week during full marathon training, and 3 days a week in between training cycles.