Adding DME to the secondary to increase SG?

I tried the brew-in-a-bag technique yesterday, and my final gravity came out way lower than I would've liked. It ended up at 1.03 vs a target of 1.06. I think this had to do with the fact that the bag was tied off at the top, thus not allowing for full grain saturation and sugar extraction. I pitched the yeast anyway and tossed it into the primary.
I'm now wondering if it would be a good idea to add some DME to the brew when I move it to secondary in a few days. I'd likely boil the DME in as little water as possible - trying to make a concentrated solution - and add it after cooling. A couple questions come to mind:

1. Would it be a better idea to do this ASAP, and just add it into the primary?
2. Is there a ratio of DME to water that I shouldn't exceed? ie, will 1lb of DME dissolve in 8 oz of water?
3. Do I need to boil for the full hour, or just enough to get the DME dissolved? Similarly, I imagine that I don't need to worry too much about hop additions (pumpkin ale, so not hoppy in the first place) - is that correct?
4. To estimate how much DME to use, can I just add up the total gravity units of the existing batch, as well as what I'd be adding, and then divide by the final quantity? I'm thinking that if I have 3.5 gallons at 1.03, I could shoot for .5 gallons at 1.2 to average out to 1.051 ((3.5*30)+(.5*200))/4. I'm not even sure that I could achieve a gravity of 1.2, or if my math above is using the correct logic, but I appreciate any advice here.

Thanks!

I'd do it in primary. Boil up some water, add add DME to the water, cool, and gently add to the fermenter. I'm not sure how much "minimum" water would dissolve the DME, but I'd say to use as little water as possible, and then stir in the DME. If it gets so thick you can't stir it, you'll have to add more water.

You only need to boil like 5 minutes, to pasteurize the extract/wort.

The easiest way to guestimate the correct SG is to consider that DME will provide 9 SG points in 5 gallons. So, if you want to raise the SG 27 points, 3 pounds of DME should work (not accounting for the water, which should be minimal, added as well).

Too many factors involved in the BIAB technique to even begin analyzing what went wrong in your grain efficiency.

1. Yes, you can do this. A lot of breweries do this technique to raise the ABV on their beers. Specifically, DFH 120 comes to mind. Jamil does this very thing on a podcast of the "can you brew it?" show, where they attempt to make a clone of a loved commercial strain.

2. That really depends on the total dissolved solids (TDS) in your water. You can probably dissolve more DME in distilled water as opposed to calcium rich tap water. When in doubt, try it and add a little more water if necessary. You're bound to get a little evaporation anyway.

3. Just enough to sanitize the water, about 5 minutes at 165 degrees f. or above. Warm it up, add the DME, let it simmer on a slow boil for 5 mins at 165 or so.

4. No idea on the maths. What I would do is use a hydrometer. Pour some of your wort into the primary and as slowly and gently as possible, incorporate it into the liquid. Then, when you believe it's mixed in well, take a sample out and do a gravity reading with your hydrometer. Continue until you get the gravity you desire. Just be sure the new wort is the same temperature as the wort in your fermenter before adding it to the mix.

1. Would it be a better idea to do this ASAP, and just add it into the primary?
You can do it anytime. The longer you wait, the longer it takes for the beer to clear.
2. Is there a ratio of DME to water that I shouldn't exceed? ie, will 1lb of DME dissolve in 8 oz of water?
Don't know. Like Yooper says, just don't have it too thick.
3. Do I need to boil for the full hour, or just enough to get the DME dissolved? Similarly, I imagine that I don't need to worry too much about hop additions (pumpkin ale, so not hoppy in the first place) - is that correct?
I'd boil for 10 minutes. Water has a lot of entrained O2, which you do not want in the fermented beer. Boiling drives it off.
4. To estimate how much DME to use, can I just add up the total gravity units of the existing batch, as well as what I'd be adding, and then divide by the final quantity? I'm thinking that if I have 3.5 gallons at 1.03, I could shoot for .5 gallons at 1.2 to average out to 1.051 ((3.5*30)+(.5*200))/4. I'm not even sure that I could achieve a gravity of 1.2, or if my math above is using the correct logic, but I appreciate any advice here.
See Yooper. 1 lb DME in 5 gallons = .009 gravity increase.