funny you should ask, i was just talking about this to someone after class today. My first dojo had a great way of teaching breakfalls, and since i like flying anyway (yes, i'm a bit lighter than 250#) i was an eager uke for koshinage...but the only instruction i got was to stiffen my legs (i think that makes the throw cleaner looking, but not really sure)...and other wise i just went along for the ride (it was a school that did NOT grab the arm or gi of nage, everyplace else i've been has you grab something).
My last dojo had a great way of working up to koshi's...first we'd do the technique ending with uke rolling, essentially a kokyunage, nage kneeling next to uke. After a while we'd move on to the same technique, but nage would be kneeling almost in uke's way while uke would roll. Next, the same thing but uke has to roll over a crouched down nage's hips. Finally we'd get up and do the technique as a koshinage.
when i told my sempai (at now my current dojo) about this he wondered how that made nages better...i told him i thought what it really did was just make the ukes more relaxed and committed to the attack, which made both nage's technique and uke's fall better. If you are afraid of the fall, you tend to hang back, which complicates nage's throw, and either or both can get hurt. You actually have an advantage in the fall due to your size, in that you are not falling from 6'6 (or whatever) but from the height of your nage's hips (usually, although my very favorite is over the shoulder so it's a bit higher) so the reality of it is you could probably nearly roll over your shorter nages. Going slowly but with commited motion (no stopping or hanging back) through the entire technique and you'd probably have a much softer landing.
Finally, since you are lucky enough to be at a school that stresses ukemi (as did my first dojo) i'd recommend the obvious--get one of the seniors to work with you on those falls
hope you have a good flight