I also currently have a 747 (15 ft) Freestyle catamaran.
We've sailed the sock off that thing for the last ten years or so.
It is a great single-hand boat that is easy and forgiving to sail and we've even run it lots of times double crewed.
We've even used it for boat camping and cruising to Catalina, an island about 30 miles off the coast of southern California.
You'll enjoy the boat, once you get it going again.
As already posted, the traveler has a single swiveling cam cleat that attaches to the hole in the forward part of what's left of the traveler car picture you posted.
That strap pictured, also is the attachment point for the bottom of your mainsheet block.
The aft end of your traveler control line attaches to an eye strap just aft of the middle of your rear beam, then runs forward through the eye strap pictured on top of your traveler car, and then forward through the swiveling cam cleat you are missing.
I tie my mainsheet tail to the tail of my traveler control line, so I am holding both, in one hand all the time, when sailing.
When you sheet in the traveler control line, the traveler car tends to center, the harder you sheet and more towards port and starboard when you ease the line.
As you suspected, unless sheeted in very hard, the traveler will run freely, from e.g., post to starboard, when to tack or jibe, until the slack in the traveler control line again becomes taunt, stoipping the car's travel.
To me that's pretty handy, however, when tacking or jibing in heavy air, I'll tighten the traveler control line as I'm coming around, so the traveler doesn't bang hard to the other side, or suddenly throw the boat hard over into a capsize.
The boomless set up is simpler and easy on your head when ducking under it, compared to a boom set up.
By the way, the several hole on the clew of your mainsail allows to affix the top end of your mainsheet block, more forward or aftward on that clew.
That helps tighten or loosen your boomless sail's foot, making the sail flatter or less flat.
I believe the original sail plan was unirigged with main only and no jib.
Those foam covered things you have on your tramp that were retor'd for a jib, were originally flat nylon webbing foot straps to put your feet under when hanging out while seated on the tramp to help stablize the boat, when theree's not quite enough wind to trap out on the trapese.
The main halyard originally was wire with a integrated lead stop that stopped at a crow's foot, located about six inches or a foot down from the mast head on the front of the mast.
When I get a minute, I'll take some photos and post them of my 747, which is still rigged mast up for its winter snooze.
Those photos will answer most if not all of your questions, but give me a week or so, the boat is at our cabin and I'm not there right now but will travel there next week.
Stay in touch, these are great boats.
I'll send a PM and give you my phone and email.
Tom
