First and foremost:
RELAX
The short and direct answer is that the factory finish wasn't smooth enough, why would a 20yo deck which has in most specimens warped enough to be out of spec for a composite HG be suitable? Also, from what I recall it's also got thinner cylinder walls than the 351... dunno about the KA.
You can try to get away without having the deck cut but it usually doesn't turn out well. Get a machinist's straight edge and check the block for flatness as per Toyota's specs. If there is ANY pitting, I'd flat out forget it and just pull the engine. Then, if it is truly flat, hit it with a precision lapping plate and various grades of diamond lapping paste until it's smooth like glass; Lap it until you can't feel anything with your fingernails and then continue to lap for another day.
Doing it this way I wouldn't trust the finish to be smooth enough to use a Stopper HG... Per HKS you need a RA of 20 or less and for some reason a lot of shops have a hard time managing that. If you go this route I would go with a MHG from Cometic... they seem to be the most forgiving and should work quite well. YOu also need to make sure the head is VERY smooth. With a composite HG like the stocker you actually want texture, not the case with a MHG.
There are a couple reasons for going with a thinner HG than stock and a couple I'd speculate on. The most common is it's a cheap (but very ill advised) way of increasing an engine's compression... Another situation where I've heard of them being used is where you want as few layers as possible (the thicker the HG the more layers it has) and then the compression is brought down with different pistons.... Then there's also the situation where the head's volume has been increased and you want to bring the CR back up.
Yes, shims. The valves are opened buy the cams pressing down on the lifters or buckets... on top of the bucket are shims which are used to adjust the amount of space between the bucket and the cams. Too much space and the valve doesn't open as much as it could nor does it open for its full duration; Too little and the valve may not close completely. In the extreme in either case you risk the cam lobes coming into contact with the shim. You also need to measure the cams... or at least measure the lobes. The details of all of this are in the Toyota Service and Repair Manual; I STRONGLY recommend you buy a copy. For now, you'll find an online copy here:
http://www.cygnusx1.net/Supra/Library/TSRM/MK3/