ok so this "dragon edition" civic is just a canadian Si (US EX) that a dealership decided to pre-rice with a fart cannon, some stickers and a set of "altezzas"
fair enough
you should currently have a D16Z6 in there
you said the engine is blown, but that doesnt tell us much...
if the top end is OK then you can do a reverse mini-me... just swap the block out for the good one from the LX keep the rest of the shit for the Si (EX) and call it a day...
you said the tranny is shot though...
this might be a good opportunity to kill 2 birds and just replace the engine and tranny...
you can look around locally for a D16Z6 swap that someone is getting rid of... or you can go online and grab a JDM D15B
torontoJDM is a sponsor on here and has complete D15Bs for $850 (CAD $884) shipped
http://www.torontojdm.com/cart.php?target=product&product_id=3273&category_id=120
just take your engine/tranny out, swap your engine harness over, put that engine/tranny in and call it a day
should be able to do it in a weekend for under $1000 including belts, fluids, beer, and pizza