I haven't had the kit in my hands - or the Heller one, for that matter. My guess, though, on the basis of the other Imai kits I've seen, is that you won't make a huge mistake if you follow Imai's instructions. The firm generally seems to have simplified rigging a bit, without turning it into an arbitrary collection of threads. (That's what Heller frequently did.)
There are all sorts of variants on the lateen rig, depending on time and place. I've seen pictures of Mediterranean lateeners that carried their lateen yards outside the shrouds. That would mean that the sail would have to be bundled up tight, virtually all its rigging would have to be struck, and the yard (which in that type of vessel was enormous) would have to be hauled around from one side of the ship to the other, every time the ship tacked. Ships from the Arab nations had a reputation among westerners for having big crews; it's easy to see why.
One thing they have in common is the necessity for resetting the sail on the other side of the mast every time the ship comes about. If the wind is from dead aft, or nearly so, they'll all be set so the yards are almost athwartships, as Viejo mentioned earlier. (The English-language term for that arrangement is "wing-and-wing.")
My one direct encounter with the lateen rig has been with the replicas of the Susan Constant, Godspeed, and Discovery at Jamestown Settlement. They were designed by Brian Lavery, a British expert who knows what he's doing, and they're sailed around Chesapeake Bay fairly frequently. On a couple of occasions the Jamestown Settlement staff has shown my students how to furl and shift the mizzen of the Susan Constant. She carries her mizzen inside the shrouds. The rigging, once you've seen it in action, is actually pretty simple. There are two tackles called (oddly enough) bowlines that run from the forward, lower end of the yard to blocks in the main shrouds. A peak halyard runs from the upper end of the yard to a block on the masthead. Two tackles called sheets control the bottom, after corner of the sail, and another pair called the tacks control the lower, forward corner. And several lines called brails lead from the after edge (leech) of the sail to blocks on the yard. Another tackle called the parral holds the yard to the mast; its ends lead to the deck.
When the ship goes about, the following sequence occurs. 1. The sheets, tacks, and bowlines are cast off. 2. The brails are hauled, gathering the sail into a loose bundle on the yard. 3. The parral is eased, letting the yard bump around a little against the mast. 5. The peak halyard is hauled, bringing the yard vertical. 6. A couple of guys grab the lower end of the yard and walk it around the mast, to what is now going to be the lee side. 7. The brails and peak halyard are eased and the sheets are hauled, so the yard gets moved back to its diagonal position. 8. The parral is hove taut. 9. The tacks and bowlines are secured. By now the ship is on the other tack.
A group of five or six lubberly college students can do that evolutionin two or three minutes. The captain told me that his regular crew can do it in less than one - though if the ship is just cruising around the neighborhood making short tacks they generally don't bother to set the mizzen at all. (I suspect the ship's diesel engine may be a factor in that practice too.)
It's not as complex or irrational as it looks at first glance. But the rig did vary from country to country, and from century to century. I have the impression that the Imai kit represents a ship from the eighteenth century, but I don't know what nationality.
The most thorough source I know of regarding the intricasies of eighteenth-century rigging is Karl Heinz Marquardt's Eighteenth-Century Rigs and Rigging - a weighty tome that's hard to find and expensive. Jean Boudriot, the dean of French eighteenth-century naval architecture, also published a volume of plans of a French chebec, the Requin. That one is probably even scarcer and pricier. If you don't want to take that much trouble (or spend that much money), I think the Imai diagrams are probably ok. A google search on "chebec rigging" will also turn up some useful images.
The pressure of the wind on the sails does indeed make any ship that isn't running before the wind heel. But I've seen plenty of handsome models of lateen-rigged ships that show the sails slack, with no wind in them. (I've always had a bit of a problem with wind blowing inside glass cases anyway - though I've seen plenty of beautiful examples that make my cynicism disappear.) And I've only seen a few heeling models that aren't in diorama settings.
Hope that helps a little. Good luck.