Thats funny. I just got that, took me a minute. Good one Mike.
Not sure of your skill level but it is understandable to not want to try and rebuild the carbs on this bike if you have little to no experience with them.
By the looks of the parts fiche, it could appear quite daunting I'm sure. See below;
[ATTACH=full]31103[/ATTACH]
But if you've been riding it it must be better, and shows that the internals must be good, so you can rule out valves (although it probably needs a valve job). Plus it sounded like it has some snort in the video, which leads me to believe that the internals are good, and that you should clean the carb and air filter.
What else is there unless your exhaust is plugged?
Used intake manifold that looks to be in pretty good shape- (offer him $20.00)
http://www.ebay.com/itm/83-honda-xl-600-intake-manifold-/272707008827?hash=item3f7e9ab93b:g:VtgAAOSwfpVZOGmc&vxp=mtr
Manifold and insulator O-rings are still available OE at RMATV
91301-428-003 O-RING (35.5X3) (NOK) $1.69 $1.52 10+ In-Stock
An OEM float is still available at RMATV
16013-KG0-891 (replaces part #16013-GC4-701) FLOAT SET - $31.42
The insulator between the head and intake can still be found used on eBay if needed.