Aligning pergola rafters to the sun?

A much simpler solution:

Build your pergola with rafters that are aligned in the most aesthetically pleasing manner to you (this is a personal preference and none of us can answer that for you). Then, once it's built, plant some leafy vines at the base of each post, or in pots near the top and train the vines to cover the roof.

As the vines grow, they'll produce leaves in the summer that will block the sun. During the winter, the leaves will drop off (providing you with some nice compost material), letting the sun through to warm the house.

Placing the rafters non-vertically will look odd, to say the least. Running the rafters at a not-parallel or not-perpendicular angle to the house will look odd. After explaining it, your more environmentally conscientious friends may be impressed by your cleverness, but, when it comes time to sell, you probably won't be there to explain it to a perspective buyer and the weird look may well put them off before getting a chance to hear about your cleverness.

Additional considerations:

• In order to allow the most sun through, you want the rafters aligned north-south and standing on edge. In order to allow the least sun through, you want the rafters aligned east-west and laid flat. You've got some diametrically opposed options there, and it's going to be really difficult to reconcile them.
• The average winter highs in Denver (Dec-Feb) is in the mid 40s (F), so you're not likely going to be spending a lot of time outside. You may grill on the back patio (everyone likes a grilled steak no matter the time of year!), but that's one or two people outside for a limited amount of time - the sun factor probably isn't that significant.
• If this is a free-standing structure not close enough to the house to notice a lack of symmetry to the house, do what you will with it! Letting the sun through to warm the house won't be a factor in this case.

Here in the Southwest arbors are built strictly for the inherent shade they provide. Although they can be constructed to provide precise shading the final design will be determined by aesthetics.

Although the top framing members can be oriented to any direction most are aligned at right angles to the house especially when built directly alongside a exterior wall.

Regarding the most effective location and spacing of the top pieces you should consider that the structure is for shading. It will most likely be useful in the summer. The winter months don't see as many or frequent gatherings outside. I think you will find most architects will design the top as (2) parallel beams connected by several slightly smaller (or equal) in size joists spaced according to shade preference. Additional shading can be provided with smaller bridging running perpendicular to the joists.

I don't have any experience to answer this directly but this might help you work it out yourself.

There is a sundial simulator which is open source, you can view it at https://tvf.github.io/sundial/ and it allows you to upload your own "sundial" model and choose any location and date you like. The upload format it understands is .obj, this should be an option in almost any CAD software.

Then if you have made an idea in CAD you can just try it out at different times of the year in your location. You shouldn't need to model things very precisely, just the horizontal beams is probably enough which should be fairly easy even if you haven't used CAD software much before. The sundial simulation allows you to rotate the model and set the height of the ground so you don't need to worry about positioning in your CAD model.

In Colorado we get plenty of sun year-round and it can be intense because of the thinner atmosphere. I've owned four homes here all purchased with orientation to the winter sun top of mind - so I understand your dilemma.
The right answer here all depends on your patio's orientation to the sun - which we don't know. At 39 degrees north the sun doesn't quite reach zenith in Colorado and is still skewed south even at the height of summer. So ideally you would want to run your rafters perpendicular to true south. Aesthetically and even functionally that may be a problem meaning that even if you get the rafters right (height and spacing) you end up shading an area other than your patio.
My best suggestion to you is to build the pergola with aesthetics in mind being aware that you want to block sun as much as possible from the southwest. After it's built add roller shades on the sides where you are most bothered by sun. Depending upon budget you can even add roof-mounted retractable shades.
Yes, it will cost more but you can add them incrementally as you see the need and you won't end up with a pergola that looks oddball. I would recommend manually operated shades. They are less expensive and more reliable.