First... you wouldn't want to have to pay for a new driveshaft... if they are even still available.
Joe is talking about the center driveshaft support. The LS has a 2 piece driveshaft... and the center support bearing is similar to a carrier bearing found on pickups that use a 2 piece driveshaft.
The center support bearing is over $200 alone... and is a PITA to change without proper tools... and experience.
The driveshaft doesn't have regular U-joints... but has rubber couplings at the front and rear... and uses metal inserts that have to be put back in the exact same spots for proper driveshaft alignment... otherwise you will have a driveline vibration and other issues.
Just to pull the driveshaft... you have to pull the rear half of the exhaust... the aluminum shield that covers the driveshaft tunnel... and mark the coupler and inserts for proper indexing... along with the shims that are at the center support bearing, (also for proper alignment.)
That being said... I don't think it is the center support... because you aren't complaining about a vibration at 45-50mph... which is more noticeable in colder weather.
I suggest looking under the vehicle and checking your transmission mount... to see if it is coming apart, (cracking, rubber deteriorating, cracked, etc.)