We purchased a used Speedster in '07. We didn't like the cranksets that were on it, so we changed out to FSA Gossamer cranks and fitted a Gates belt while we were at it. We've gone back to a chain now. The FSA BBs are only so-so IMO. We went through the first 2 sets of bearings fairly quickly and they have some drag from the seals. We're running Phil Wood bearings now, apparently successfully. If your current cranks are an acceptable length and they spin smoothly with little drag, I'd leave them alone. Plenty of time to look at options after you wear them out.
The bike luckily came with a WoundUp carbon fork, and we like it very much. I'd give it a definitely worth-while. Other carbon forks might be too tight for touring tires.
Not so much carbon bars. We've been down a few times, though no injuries, and much appreciate the aluminum. Stoker's bar always takes the hit.
If your stoker is losing power because of bouncing on the Thudbuster, then a carbon post might be worth it. Otherwise not.
As others have said, our biggest bang-for-buck has been tires. We're running 25mm PRO4 Endurance. 290 lb. team.
We tour loaded on 28mm tires, but we really worked to get the weight out. Total added to the bare bike weight for loaded camp-touring is 43 lbs., with rear panniers, bar bag, small frame bag, and captain's saddle bag. We cruise at only .5 mph slower on the flat, loaded.
We're in the process of changing to Kinlin 279 rims and CX-Ray spokes, same Chris King hubs the bike came with. Have the new front on. That seems to be a worth-while change, too, and not too expensive. I build our wheels myself. Not that hard and at least as good as pro.
Another place we got a lot of bang for very little money was in position. Captain is running a slammed -17° stem. Stoker also has a slammed, short stem. Stoker bars are completely under captain's saddle. That's absolutely huge.
The biggest bang, though, has been in conditioning and rider weight. We're down almost 20 lbs. since we bought the bike, and our power is way up. We could lose another 15. It has taken us a lot of tandem riding and communication to get the team power up. We're a completely different bike now from when we started tandeming. Getting the power down on the road is the thing. Synchronicity, standing, no rider motion, all that stuff has made a big difference.
So bike weight, per se, is almost irrelevant in the above list. So many other places to find extra speed. Once you've done all that, then maybe bike weight might, I say might, be important.