Hi, Pete. I read your question a couple of times, and I'm afraid I'm a bit unclear about whose genome you're looking to simulate, the father's mother (shared with the aunt) or the father's father. If the mother, you're best bet might be to look at the GEDmatch Lazarus tool. But to get good results, it takes some planning in advance. To save G2G space, I'd point you to a website if I knew somewhere this was fully discussed, but I don't.
If you haven't used it, it requires at least one direct descendant of the "pseudo-genome" to be created. Ideally this would be a child (which you have) but one or more grandchildren can also work (but don't use both; if you have a child's kit to enter, don't also include a grandchild). If the spouse of the target Lazarus run has a kit number at GEDmatch--and this can certainly be a kit created via phasing--you should enter it to help the tool differentiate between base pairs contributed to the child.
The trickier part comes under what's labeled as "Group 2"...and there's a reason they have entry fields for a whopping 100 different kit numbers. In this group you need to enter GEDmatch kit numbers for people directly related to the Lazarus target but who are not direct descendants. As examples, GEDmatch gives: "siblings, cousins, aunts/uncles, or parents." Brothers and sisters, full or half, are clear enough, as are parents, if in the rare event someone is trying to create a kit where the parents have DNA on file.
But aunts/uncles and cousins, in my personal experience, is where the advanced planning comes in. I'd point you to a website if I knew somewhere this was fully discussed, but I don't. So two caveats. First off, recognize that the resultant Lazarus output may not end up representing a parent, but would still be helpful in your search. As GEDmatch says: "If close relatives are not available, distant matches can be used in Group 2 but less Lazarus DNA data will be produced--you may still be able to create a virtual cousin instead of the hoped for virtual parent."
You'll need enough shared segment information input in order to build the new kit. I don't believe GEDmatch tells you that up front, but that minimum threshold is 1,500 cM in order for the new kit to "synthesize" and go through batch processing and make it usable for one-to-many or other comparisons.
Second, and a qualifier of that, you need to plan the kit input to make sure those cousins are coming from the Lazarus target's line of descendancy. In other words, if you're trying to re-create a grandfather (as strange as that sounds) on the father's side, you do not want to use cousins who are related to the child via the grandmother's family. The Lazarus tool really can't tell the difference between chromosome segments coming in from one line as opposed to another.
As an example, I recently I tried to help someone whose father was adopted. We had kits for the father, the mother, the child (the person I was helping), two grandchildren, plus a 1st cousin of the father, two 2nd cousins, and two 3rd cousins. Lotta material. The problem was that--unbeknownst to me up front--all the cousin's were from the father's mother's side of the family...who would have shared no DNA (ostensibly) with the Lazarus target, the father's father. Sure enough, the kit generated just fine. But in testing it afterward, the person I was helping said it was turning up matches that were suspicious, that were already known cousins from the grandmother's side of the family.
I had simply taken the kit numbers supplied and run them through the Lazarus tool. Save yourself some time and don't make my mistake. We had to start over at the place you should begin: clearly chart out--draw a little family tree sketch if you need to--who the Lazarus run is expected to re-create, and where all the known kit numbers fall with respect to the target's lineage. Kits for input need to be screened so that you absolutely know they're in that same line of descendancy, not from a spouse's.
Don't trust the family history only. Run one-to-one and triangulation comparisons in advance to make sure the Lazarus kit will see no unrelated input. In the example above, what I ended up doing was throwing out all those cousins, and based a second run only on kits from unknown cousins who had been triangulated to relate to the father only, not the mother, and at a minimum cM threshold of 15...false positives are just too likely below that. We got a kit generated, but it didn't represent the target grandfather's genome. It was still a level of refinement, though, on that particular line we were attempting to identify. Which leads me, finally, to...
Check your work. After the new kit completes batch processing, run it through a bunch of types of comparisons to make certain it does not match kits you know it shouldn't (in this case the cousins initially supplied), and does match kits you think it should. Make careful note of the shared cM among known relations so that you can evaluate at what level the new kit represents a biological relative. Our new kit came in showing about 650 cM in common with the father's child, placing it somewhere between a great aunt/uncle and a 1st cousin 1x removed; matching with the father's grandchildren was roughly consistent with that.
In the example, we didn't end up with a grandfather, but we ended up with something approximately like a half-great uncle. Not what we were after, but still useful for future research nonetheless.