One idea could be to lie face down on the floor and pull yourself forward just using your hands and push yourself back again, just using your hands.Repeat. Or 'swim' across the floor by lying face down and doing a butterfly stroke type movemant with your arms , then pull yourself along when your hands hit the floor. Not as hard as pull ups but just some ideas.
lots of people have not read to OP. play parks can be a godsend for travelling, ample training opportunities there. if you are going to look at suspension kits i prefer blast straps to TRX plus they’re cheaper. i've been known to do high rep pull overs with my suitcase/hotel furniture too, can get a decent pump wont do much by means of ax strength development
I do not know where my thing about One-Hand assissted pull-ups went but I find that it is replaced about injuries. I came back to add that you can use this pull-up station to do half-bodyweight pullups, resting both feet on the step with both hands close together but not touching, maybe two inches apart. But you are not going to talk me out of that controversial training. I will call collect if, but I wont, from the hospital to tell you "You are right!" I have been already doing it for awhile.
Now, I know what you are talking about. Facing-Foreward Strictly like some Strict Form as people describe as Pullups! I do mine loosely as your body settles spinning as you hang from a rope. With a rope you spin, but with the karate-belt-bar you don't. The hanging should be natural. My palm faces towards my ear, cheek and almost neck at the top. I always start at the bottom, always Limp to get the natural "feel" and go up slowly. Probably doing some twisting along. Don't want to come back. Go ahead Delete!
I am a huge fan of aussie style pullups. http://s20.photobucket.com/user/Enzuguri/media/xc_inverted_pull_ups.jpg.html Get a door jam pullup bar and you can do this anywhere