I recommend the normal Trans America route with some improvising if you want to cut the distance a bit. First place to cut is using a different starting point. Their alternate of Florence is nice. I have found that it is pretty easy to shorten AC routes in general.
70 days is doable without any short cutting. We took 73 days and it could be done a good bit quicker, especially by a couple young and fit guys.
The TA or any tour can be done pretty cheaply and on any reasonably reliable bike. I strongly advise not getting caught up in the notion that you need a lot of the stuff that is often touted as must have. If you do get a new bike one inexpensive option is the Windsor Touring ($599 delivered). If you go that route either go over the wheels carefully or have someone do that for you. That said what you have may be OK.
I also advise packing light. I took 50 pounds of stuff, on the TA but that was gross overkill and I was repeatedly mailing stuff home. Since then I have gradually gotten into going ultralight and like it a lot, but it isn't necessary to go that far. Still I'd advise applying some of the principles of that approach. Maybe shoot for 20-25 pounds, but set a hard limit at 30 pounds of gear weight including panniers, but not food and water.
There is no need to go high dollar on your gear. I have a bunch of fairly high end gear and not counting clothing It was about $1000 total. I did a list of cheaper alternates and It came in at $330 for full price items mostly from REI. Going with sale prices and shopping carefully could cut that even lower.
I will suggest a couple articles I wrote and also our journal on the TA as possible resources. My
article on ultralight touring has a section on going ultralight on a budget. It might be helpful even if shooting for moderately light touring. My
article on frugal touring should be helpful as well. Our
TA journal was from the perspective of three first time tourists doing the TA so it may also be appropriate.