I posted a month or so about taking trikes on the DART to ride in more remote locations.  Watching a Youtube video about dis-assembling a Terratrike Rover, I figured out that taking the seat off the Rover will make it much easier to get on Dart.  Removing the seat takes just a couple of minutes, and you usually have to wait a little while for the train anyway.  When you have the bare frame, it is much easier to stand directly behind the back wheel, lean straight over, grab the two front wheels and lift them straight up.  Then you are rolling on the back wheel and steering by turning the front ones.  You can easily roll on to the train and use a bungi to loop through the front wheels and into the hangar straps in the wheel chair/bike space.  I made a velcro shoulder strap to hold the detached seat on my back while I get on an off.  the seat goes back on in a few seconds and you're off.  Be sure to use a Sharpie marker to mark the position of the seat before you remove it, so it goes back in the same spot.  I am contemplating fabricating a folding seat for the Rover - one that will fold flat against the frame, making it equally easy to get on and off the train w/o removing the seat. Let me know what you think.

I take my bike on the train frequently.
If there are other bikes on board or it is crowded you're going to be in a heap of trouble.
 
 Fully half of the time the wheelchair/bicycle/elderly seats are taken.
 
 When they are taken frequently one has to negotiate in a most awkward fashion to get access to the hangers. I sure would want to do that while I'm juggling my seat under one arm and my bike on the other.

Yea for DART!
If the train is empty or  <1/3 full , shouldn't be too bad.
But….
Any more , you have a race to get a platform level door and get past
any other bikes and the other travelers, who tend to stand by the doors and sit
in the folding seats by/under  the bike hooks.
 
One has to negotiate with the patrons , who would have moved if they read the signs
and get the bike/trike up before the train starts,
often within the 30 seconds after you get on. Time is tight.
 
Again, most will move, if asked, but it is often awkward and slow.
Especially if there is not an immediately adjacent seat for them to go to.
Unwedged in or unstraddled, bikes are a handful when the train rocks.
An unfolded trike would occupy almost the full area between the two exit doors.
 
It can be tight, even if you have a straight shot to the hanger hooks.  
My last trip on the Orange line out of the first West End stop  
had me, two other bikes, and an accompanied stroller competing for space.
Had there been an impaired or elderly person there, then no way , ouch.  
Had I tried at the other end of Pearl St, I would have to displace a lot of folks
As it was I had my hands full with a 20" Dahon folder
This at 3PM, hardly rush hour.
 
and I don't have your negotiating skills
 
 
I'm a big DART fan/user and have tried to get my Trident Folder configured for the train
but it really would need the front wheel or post strap idea of the OP, a carry sling , seat sling or strap, and a guard for the chainring
(and probably a Disabled sticker and lots of empty seats)  to make it happen.
Do-able, sort of, maybe.
A 700Cat at 25 lbs would be lighter to tote , but still has a  sharp, greasy  chainwheel to maneuver though your fellow riders.  
I would anticipate a similar problem with 2wheel cumbies
 
I am looking forward to the Trident and Terratrike super folders, because it would be way cool togo to FtWorth or even Austin that way.
I may still see if my Trident can be configured with the BOBtrailer to roll it into the Amtrak luggage area or wheelchair space
A regional pass gets you to FtWort and Denton, cool day rides.
But have to use upright folders unless a BikeFriday  Saturday comes around again.

I did a little research and found that CalTrans has made special cars for bikes, the Bombardier and the Gallery car.  They put a couple on their heavily travelled routes and bike commuting has burgeoned.  Google it.  Very interesting.