...the 630 is in addition to dragging the clutch all over the place in gear...
I will try the weight oil.
...
I did not know there was a clutch rod recall...
We had a significant discussion about the matter in this thread:
http://www.cafehusky.com/threads/clutch-rod-an-oil-change.22695/
That thread is specifically about the clutch rod recall/TSB, so I'm not sure that I understand how you didn't know about it. Furthermore, in that thread I recommended that you change the oil to 5W-40 or 10W-40 (the poster in this thread recommended Rotella T6 in 15W-40, but it is only available in 5W-40, so I presume his post was a typo). Did you try that?
Finally, you stated in the other thread that Solid Performance had your bike. What was the outcome of that service visit?
I would not measure shim thickness with calipers. A micrometer is the only proper way to measure such a thing, IMO. Luckily a 1-inch micrometer is inexpensive, and they are very accurate and robust. I also have one that you could use if you like.
It's not necessary to buy a complete kit, unless you can't handle having a bit of down time. The normal procedure is to measure the valve clearance, and then if a change is necessary, disassemble the head, measure the shims, and order the size(s) you need. Any Husky, Yamaha, etc shop should stock a large assortment and a decent shop will let you buy individuals.
IMPORTANT NOTE: The first step in all this is simply to MEASURE the valve clearance, before you tear anything apart. This is done by removing the cover(s) (not sure if the 630 has small inspection covers like the 610 or if you just pull the whole valve cover as a unit), putting the engine at TDC, and measuring the gap with feeler gauges. Only after you do this should you bother disassembling the engine and shims.
As a more general comment, while a compression test isn't a bad idea, I would not trust it to properly diagnose tight valves. Valves can have clearance (and therefore good compression) on a cold engine and yet get tight and cause starting problems on a hot motor. I suppose you could do the compression test hot and cold... In any case, I think that the valve clearances should be checked in the case of problems and at whatever interval Husky recommends.
There are a variety of other possible issues related to the hard starting (temp sensor, air filter, spark plug, mixture, idle setting).