2:53 is a rather fast 800m rep time for somebody targeting a 3:15 marathon - I suspect you're doing too few reps and/or too long a recovery between to get the benefits. I built up to 8x800m averaging 3:00 when marathon training (race result was 3:04:3x).
7:50 min/mile is also too fast for long runs for a 3:15 marathoner, and 26km is too short for a long run unless you're quite early on in a plan or it's a cutback week. My long runs were ~8 min/mile with about one in three of my long runs having a fast finish.
And 7 min/mile pace is bonkers pace for an 'easy' run at your level. Hopefully the treadmill is wrong and you are actually doing around 8 min/mile pace, otherwise I fear you will burn out by race day.
Thanks for the compliments, but really the first chunk of improvement is the easy bit once the initial motivation is there. Now on the shallower tail of the diminishing returns curve, trying to cut another 10-20 seconds off of the 5K PB takes much harder work. There are people with less natural speed putting in a lot more effort than me, and there are people I know with more natural speed and talent than me who continue to improve rapidly and leapfrog me after I've started to plateau. It's hard to see where you are at since you don't seem to have any race times to judge from?
3:57 to 3:15 looks like a large difference, but the last September marathon sounds so badly planned/prepared that it's difficult to read much from it.
Do you have any recent shorter race times as a guide to support your 3:15 goal?
Saying that you "exceed paces from training plans" can be a good sign if you're referring to hitting faster interval session or tempo run paces, but if you're running all or most of your long runs too fast then that will have a detrimental effect for most people.
In answer to your actual question, my largest improvements, as is the case with most people, were when I first started regular training and racing. In 9 months I went from 24min 5K to 18:19 5K, and from 49:40 10K to 39:30 10K. But in the two years since I've only shaved a few seconds off of the 5K time and a couple of minutes off of the 10K time.
I try and hit 'race weight' for important races but it's not a weight I can sustain long term and be healthy and train well.
I do this too, maybe 2-3 times a year I'll bother to drop the extra ~2KG above racing weight, that I tend to carry when training normally and treating myself to some red wine and chocolate when I feel like it.
This seemed to work for my marathon and HM PBs. However my fastest of four 10K races so far this year was actually at my heaviest - mainly because it was the best weather of the lot. ie once fairly lean and fit, all the other variables on race day are much more likely to make a noticeable difference than 1-2KG either side, so whilst it might help you'll never know for sure.
But Tom you're talking about losing 16lbs in 3 weeks, which is equivalent to 56000 calories in 21 days, so a calorie deficit of around 2600 calories per day. That's not possible to do healthily, especially for someone already at a healthy weight. The 5 pounds lost already is probably mostly your dwindling glycogen reserves being used up and the associated water weight that will have been shed with it, it's extremely unlikely that you would have lost 5 pounds of fat within a week unless either by starving yourself or by eating normally and running a 20miler every day!
I followed this plan last year and I always took the Tuesday run to be intended as a similar pace to the Monday and Wednesday easy runs, since they are labelled the same on the chart, although occasionally I would be in a rush to fit these in around work so ran some closer to MP+30s than my MP+60s easy pace.
With the cumulative fatigue from the Thu/Sat/Sun sessions, especially in the later weeks, I don't think there's any value in speeding up the Tuesday mid-long runs - better in my opinion to recover well for Thursday than to compromise the intervals or hill sessions.
At the end of it I was successful in my goal of running a GFA qualifying time for London, which was a decent conversion from my HM PB at the time, so this approach worked for me at least.
MFP and Garmin have always given me similar calorie estimates to each other (around 110 per mile for me), so assume the problem here is most likely a mix up of values or units being chosen in MFP. Or less likely but still possible is a bug in a particular version of MFP.