You can think of basal area that way. I've usually worked with it as a single number to describe all trees in an entire stand: this area of forest has 80sqft/ac stump surface area if we cut it all at 4.5ft high (standard height, 'breast height', to measure tree diameter). Some foresters use a single number describing only the marketable trees in the stand, merchantable basal area. You could also find that number on a per species basis with forest sampling methods, but you can probably get by without that much detail. It's more to figure out overall density and desired density (e.g. basal area of 70sqft/ac total is generally considered a good density for growing timber, so when density gets up to 100 and higher it's a good time to cut it back to 70). That sets the medium-level goals for silviculture prescriptions.
As for how you change the density, those low-level details are the prescription, and seed tree approach is good for creating a savanna feel. It's less forgiving than shelterwood, but the fact that you're a landowner-operator working on a small-scale makes up for that as I presume you'll take more care in what you cut vs leave.
Sounds like picking the seed trees is what you're most unsure of. Prioritize good genetics and species composition for what you want the future forest to look like. Make an effort to remove the bad genetics. This is the opposite of greedy logging: short-sighted folks will take the good stuff and leave the bad, but the best forestry is taking as much of the bad as you can and just
enough of the good to pay for the operation, limiting yourself to ensure enough good genes are around for regeneration. Also think about spacing of those genetics, that's where basal area comes in. The change in basal area you desire can translate to how many trees are kept or removed in a cluster of say 5 or 10. That way you walk around and 10 trees at a time decide which to leave or take, then walk away and decide for the next cluster, do that systematically and eventually you should have an evenly spaced distribution of good selections getting you to the overall desired density.
Those old huge trees are great. Some standing dead
wood is good for wildlife too, but that needs to balance with the need to mitigate hazard trees.
Lastly for deciding what to take or leave, consider if you want more even-aged or mixed-age future forest. It will be mixed-age unless you really try to even it out. But in seed tree you could be selecting an ancient tree to keep in one cluster, a middle-aged one in another cluster, a young adult in another etc. so the woods will develop into quite a mix over time until the next major disturbance.
As for regeneration with seed tree, I don't know how silvopasture will affect the regeneration from that cut. I've done seed tree cuts and seen results of past seed tree cuts, it can be really nice. One beautiful tree over here, a small cluster of great genes over there, pouring seed out on top of an existing seed bank now released - like a much sparser 'shelterwood' cut, as shelterwood has strips or larger clusters to reseed rather than seed tree's sparse individuals or small groups. Thing is with silvopasture, livestock might hinder natural regeneration or affect the seed bank somehow. Probably if you're hands on about it, planting trees and protecting them from livestock during establishment, it's a nonissue. Just something that comes to mind. Wildlife have an impact on natural regeneration for sure, but I bet it's a different kind of pressure on the new trees in intensity and timing than silvopasture.