I used the centerstand on my '00 LT all the time. It is mostly technique but the ease of the process is sensitive to the height of the bike as I could tell a difference when my tires were worn. Put new tires on and it was easier. That was before I got on this forum and read so many accounts of guys finding it easier after changing their rear shock absorber (strut), which also raises the height of the bike. Changing the height changes the amount of leverage you have in the lever/fulcrum application of the centerstand.
My technique was to put it on the side stand, then get off the bike. Stand on the left side and depress the foot lever on the centerstand until it touches the pavement then lift the bike while holding the left handlebar and the left sidecase handle. I found that hand position better than using the grab handle under the left side of the seat. Gently rock the bike side to side to be certain that both feet of the centerstand are touching. Then mash the lever with all your weight. In my case that was about 215 pounds, sometimes it was the right foot sometimes the left, depending on how my plantar fasciitus was doing on that day. Never put it on the centerstand on a surface that uneven side to side. It is OK if the surface is slightly uphill or downhill. Uphill is easier than level and downhill is harder. My bike always came up on the stand, even though it sometimes took more than one attempt, and I never dropped it while putting it on the centerstand in more than 40K miles of riding.
Regarding the stability of the bike while on the cernterstand, it is stable enough that you can stand on the peg and swing your leg over to mount the bike, just like stepping into the stirrup to straddle a horse. It is pretty stable, even though it may not look like it.