Does this sound like 6 gear synchro problem
 

This is the first time my car has been out in the cold ~ 38 degrees.

The transmission was a bit stiff, but this seemed normal when cold.

While driving the transmission got stuck in 6th two occasions. One of which required a forceful knock of the shifter to unstick it.

Now in order to get into 6th I have to make two quick hits of the shifter into sixth. If I try to shift into sixth it wont go, but if I quickly try again it goes right in. With the car motionless I get get into all gears, included 6th smoothly.

Try double clutching to get into 6th, does that help? If not, it sounds like something in the linkage/fork.

I've heard of double clutching, but exactly how is it done? I've never actually learned how to do this.

I had a nice response written, but my router decided otherwise...

double clutching = rev matching. Basically, clutch in, shift from 5th to neutral, clutch out, rev the engine to match your expected 6th gear RPM, clutch in, shift to 6th. We're basically taking the input shaft and speeding it up so that the two gears that mate for 6th gear are spinning at the same speed when you make the shift.

Try it like this: While cruising down a long stretch of road where you arent worried about cars behind you (country road/freeway/etc) and in 6th gear already, look to see what RPM you are travelling at given your current speed and remember it, then shift down to 4th, wait a couple seconds, shift up to 5th, wait a couple more seconds, make sure you are at/slightly above the exact speed you were travelling when you were in 6th gear earlier, then shift into neutral, let out the clutch, rev up to the RPMs that you remembered from earlier, and then clutch in, and shift to 6th. You should do it quickly enough that you can shift into 6th while the car is still moving at damn near the same speed that you were travelling before. If it takes you awhile to get your RPMS perfect, then add another 5 MPH to your pre-shift speed so you have more time to match your revs as the car slows in neutral. Ideally, it should shift like butter.

Another thing you can do, with regards to shifting OUT of gear. While crusing in 6th gear, apply slight but firm forward pressure on the gear selector, then simply let off the accelerator pedal without applying any clutch pressure. Done right, your shift lever should effortlessly slide forward and into the neutral position as the gears in the transmission transition from input-loaded to output-loaded.

Lets also test for abnormal loading on the input shaft of the transmission. While stopped and in neutral and clutch engaged (not pushed in) , rev the car up to around 5500 rpms, then disengage (push-in) the clutch and tell us if you hear any funny noises. This is probably best done in an open garage or with a friend laying beside the car because the cabin is likely to be well insulated against transmission noise in an open environment. Here, we're testing to see if any bearing surfaces on the input shaft are damaged, its highly unlikely, albeit possible, that your input shaft is experiencing an unnatural load and reducing RPMs due to drag somewhere along the input shaft. My experience is that the 6th gear synchro is indeed shit, and would probably go out for this reason LONG before the other gears did the same. Inspecting your magnetic tranny drain plug for significant amounts of metal shavings is a MUCH better way of doing this, but it requires that you drain the tranny and then refill. To be completely honest, I pulled this entire paragraph (except for the magnetic drain plug part) out of my ass, but maybe it will work?