I can't say for the time, but if you go east to west, start in the fall when the chances of heavy headwinds on the western section will be less. I suggest an early spring start in the west to take advantage of the sometimes awesome tailwinds. This are pretty consistent and can be spectacular. I wouldn't want to fight them in the other direction. I think a Feb. start would be best if you could manage it.
To calculate days, just figure what you can comfortably manage yourself on a day-to-day basis and do the math. What's comfortable for one could be slow or fast for another. I trike a lot, and as you must know, triking is generally not as fast or efficient as two wheeled travel, so I work that into my calculations. Looking at roughly 3,000 miles, 49 days means about 60 miles/day, no rest days. That's not a pace that I, personally, would want to maintain. I like a rest day, exploration days, etc. Also, consider the major climbs in California, AZ, and NM. You are the only one who can determine a good pace for yourself. Have you toured a lot on your trike? If you want to make good daily mileage, I'd lose the BOB trailer and work on a system that lets you carry what you need on the trike alone. This is not hard. Here is a link to my Crazyguyonabike journal from my triking tour down the CA coast last summer. The picture shows my Catrike Expedition with large Radical panniers, Arkel rack trunk. I strap tent and sleeping pad on each side of the trunk http://www.crazyguyonabike.com/doc/page/pic/slideshow/?o=RrzKj&pic_id=772169&v=0
. I can carry plenty of gear this way and used an identical setup for a cross country ride on a HPVelo Street Machine. You will save over ten pounds in weight this way--no joke! What does the BOB weigh, 13 lbs? Plus an extra tube, etc. If speed is important, don't take it.
Personally, I'd want 60 to 65 days for a Southern Tier. Some days you'll want to hammer big miles, others you may want to ramble. Bad weather, gear problems, etc can alter the pace a lot, too. If at all possible, avoid being to rigid with a schedule.
Have a great ride and report back!