I can't speak for ACA but I would doubt they intentionally factor in recumbent trikes for a route. They most likely factor in daily traffic volume, shoulders, etc. along with services. I am sure they would like low traffic roads with shoulders but of course, you can not always get that.
My wife rides a recumbent trike. For grins, I took it touring one time from Milton, FL to Galveston along the coast. Extremely comfortable but definitely slower.
Not truly a comparison to the TA, ST, etc. but I did not feel overly uncomfortable riding it except in New Orleans and maybe a stretch here or there . I did use two BRIGHT flashing HEAD LIGHTS (NiteRider 750); one facing front the other back. A touring buddy said he could see the flashes literally, not figuratively, just under a mile away. I highly recommend it. Just angle them just slightly down so not blinding the drivers. Down side is the lights need to be recharged nightly so electrical (or a big power bank) would be needed. It took about 4-8 hours to fully charge them while charging them both simultaneously. I would typically only keep the rear facing on while riding unless in an urban setting so the front could be used as a backup. I also had a flag on a pole to assist in being seen.
While I have not ridden US-60 east of Wickenburg, I have driven it between Wickenburg and Louisville, KY. I would say, overall, that would not be a bad option. A few parts would not be fun traffic wise, i.e. eastern Oklahoma due to rumble strips in the shoulder, parts of Missouri (no shoulder and high traffic but there are reasonable alternatives though). The further east you get, the heavier the traffic so you would eventually need to bail to smaller highways.
I would encourage you to review each state's AADT Map showing the daily traffic volume for given highway. Bookmark the websites and look for alternatives when a road with no shoulder gets too busy for you.
I would ride whichever route you feel most comfortable with. All things being equal, I would prefer a low traffic (<1000 a day) with no shoulder (assuming reasonably good line of sight) over a interstate type road. Ideally, a low traffic road with a 3'+ shoulder would be best but I haven't died and gone to heaven yet. A 4-lane highway with 6000+ cars a day with no shoulder may be better than a 2-lane road with 3000+ a day. It is sort of a give and take choosing which route you pick. You also need to guess is the traffic constant or is it high only during rush hour.
You might try reading a few journals over on CrazyGuyonaBike.com and see how the trikes handled the TA.
A word of caution. When riding the ST, do NOT ride between Brawley and Blythe on a Friday thru Sunday (extend if a holiday weekend). TONS of large RV's pulling trailers filled with dune buggies heading to Glamis from both directions are speeding by. There is no shoulder and the road is not overly easy to "bail off" on. Lots of dips where a trike could get "lost" momentarily.
When you get to Blythe, eat at Garcia's Mexican restaurant on Hobsonway. One of the best Mexican restaurants I have been to (and I eat it once a week minimum).