OK. I have a little insight that might help. I've been a coach for a number of years and often have to figure out how to get someone back into shape pretty quickly because they've been injured or didn't do their homework over the summer, etc...
What I call my "sure fire short cut trainging for short term success" (I acturally just made that up right now) came around kind of by accident. When my son was born, I found that I had very little personal time. During cross season, I'd barely been able to run at all. Once cross ended, I decided I wanted to start running a bit more (maybe mid december). The problem was that after teaching, then coming home and doing paternal duties, I often would only be able to get out the door to run after the wife and kiddo had gone to bed. I had a couple of 3 mile loops around the neighborhood that I'd go out and run at 9:00 pm. Basically, I just started jogging pretty easily but as my legs warmed up, I'd get into the fastest possible pace I could manage without feeling any discomfort (probably just a fraction below true tempo/LT pace). That is about all I'd do. I was getting maybe 15-20 mpw that way and I really don't know what kind of paces I was actually running. After about 6 weeks of that, I decided to enter a 5 mile road race. After signing up for the race, I had I think 2 weekends where I could do a "long run". Those ended up being about 7 miles and I did them pretty fast after running easy for a mile or two.
When I got to the race, I didn't expect much. I had only run something like 17:45 for a 5k about 4 months prior to starting back up with the low mileage thing I described above. I hit the first mile at 5:38 and was really surprised at how easy it felt (I felt like I was running much slower). I held about 5:45 pace for the next 2 miles and hit the 3 mile point at about 17:20 ish, still feeling OK. I died super hard about 0.5 miles later (because, hey, I was already way out past my normal run distance), but still finished in 29:50. I think you could use a strategy kind of like the one I did by accident to get yourself ready for this corporate thing.
There are a ton of terms to describe that pace. I like Lydiard's term, "Highest Steady State". I shorten that term to "Steady State" with my teams. Others will call that pace "Tempo" or "Sub LT", but we'll use "steady". I think steady state pace gives the best training stimulus while still running at a pace you can do on a regular basis.
The exact percentage of your total mileage that you will run at your steady pace will vary based on how many miles you are currently doing. Suffice to say, you need to run steady state and you need to make it a big chunk of your total mileage. Just run to the point of discomfort, then back down again. Pretty soon, you'll be able to zero in on the exact effort level that you need in order to get the most bang for your buck. I wouldn't try to go too far at steady state pace, probably no more than 20 min in a given run, maybe more like 15. But I would try to run at that pace almost every day. See how that goes for 3 weeks.
That's not exactly what I do with the athletes that I coach though....so, here comes option 2 (which will also work pretty well. I know this because this is what I do with kids who have to get in shape in a short time). Option 2 is a lot like option 1. Very frequent sessions training at near LT pace. In option 2, I have my kids run just a bit faster than LT pace, but break it up into intervals. A real common workout for my kids who run around 17-18 minutes is 800m intervals on the track on a 4 minute cycle (start an 800 every 4 minutes). They do these a bit slower than 5k pace and they do them 3-4 times per week. So, if I have a kid who I think should be in 17:30 shape by league finals and have say, only 6 weeks to get him there, the progression might look like this.
Week 1: 3 workouts on the track of 4 x 800 @ 3:05-3:10 starting an 800 every 4 minutes:
Week 2: Same as week one but the 800s end up being more in the 3:00-3:05 range.
Week 3: I might move the kids to our cross country course and do 3 x 1200 on a 6 minute cycle or I might go 5-6 x 800 on the track
Week 4: Will certainly be at 6 x 800 by this point (probably right around 3:00, maybe some dropping into the mid 2:50 range). If doing 3 x 1200, we'll jog back to school and do 4-6 x 200 at about mile pace with about 1 minute rest.
The last 2 weeks, I'll have the kid do the regular team workouts, but just run very easy on the other days. So.....
Week 5: 6-7 x 1k at goal 5k pace with 2-3 min recovery, and a 25-30 min steady/tempo run
Week 6: Taper down. 3 x 1k at significantly faster than 5k goal pace with 5-6 min recovery (done maybe 4-5 days prior to race). A seperate session of 6 x 200 at about mile pace with about 1 min recovery. (maybe 2 days out from race).
Neither option 1 nor option 2 are ideal for long term success, but should get you fit quick.
Good luck and check back in periodically. Interested to see how it goes.