A Conservatory is not expected to follow any of the architectural elements in the parent house, so it can break all the constraints and still look good.  Choosing something for the other side would mean building a custom addition out of custom-made parts or deciding to accept some of the elements not lining up.  

The E1600 New England Colonial additions have the same roof angle as the Painted Lady (although the peak is side-to-side) and a foundation match. They include a door pad to mediate the floor thickness difference. The floor-to-ceiling does not match so the second floor won't line up with the house, but a door into the house might use a step to accommodate that. The New England additions can be custom-ordered with a blank front (no window hole) so they can be more easily customized by a builder to use Painted Lady windows.
Here are the instructions for the E1600 for your reading pleasure in case that would be helpful. 

Let’s do the same kind of analysis for the DH37K:
The first thing to note is that the 37K is built entirely differently from the Painted Lady.  The DH37 has the walls in between the floors, and the floors stick out past the walls.  For an addition, that means the main house for which the addition was designed does not have a smooth wall - it has floors sticking out, and the dimensions of the parts for the addition use that ‘sticking out’ of the house floors as part of the fit.   When putting the addition on a house without ‘sticking-out’ floors, the addition’s floors will offset toward the house wall, and won’t have a centered ‘sticking-out’ of their own.  One solution might be to shorten the width of the addition’s front walls by the same amount (3/8) to re-build the right amount of ‘stick-out’; another might be to add pieces to extend the floors the same amount.

The floor-to-ceiling of the DH37K addition is 10”, but the above construction style gives the opportunity of cutting the walls to 9¾ to match the floor-to-ceiling of the house.  That’s an easy customization.

The foundation height is the same: check!

The base floor thickness issue exists here too, but the DH37K addition’s floors do not fit into grooves as they do in other houses and additions (and as they do in the Painted Lady) so an upper floor could be used as a Base Floor, and then the tops of the floors would line up too.  The thinner Base Floor could be replaced or it could be used for the top deck where it is on the outside and less inviting of comparison

The height will bring it into conflict with the house's roof which could be trimmed or you could change the 2nd floor's walls to one that shortens the addition enough to will fit under the roof.

Painted Lady window panes are much larger than those for the DH37K and finding a cropping that would leave a nice print might be challenging. A customizing builder could re-cut the window holes to accept Painted Lady window parts, though.

Finally, I have cut material for those who choose the ‘customizing’ avenue, but they have done the design work and are only looking for material that matches that of the Painted Lady which they then cut, groove, bevel, and shape to their design.  They give me a cutting list for the materials but they are the ones who make the Addition's actual parts. If you have the wherewithal to do those things, we can talk further about materials.

Best wishes
Gary