A guy up in Alma told me, as of yesterday, Mosquito pass was closed with snow about 6ft deep about a mile from the summit on the Alma side. I don't know if you can reach the summit from Leadville or not, but it doesn't sound like you can go all the over to Hwy 9.
Halfmoon is a fantastic trial. Champion mine is an amazing site to see. The amount of steel that was hauled in for mining opp is wicked impressive. There is also another trail on the left just before you reach the mine, it's a bit tight in one section but careful tire placement you'll have no worries. From the top of that side trail you can see Independence pass.
Have not been to Halfmoon this year... Also the deepest of all the water crossings (strongest current) is the trail to iron mike's mine. Plus there is a small rock garden with a minor creek running through it on iron mike's, which makes it difficult with a stock jeep. Your Undercarriage will become very intimate with the rocks. I would just stick to the champion mill trail on Halfmoon.
I really didn't see much on the way up. Apparently, it is all on the Alma side. I talked to a couple of hikers who were heading down that way. The Alma side was closed due to snow and won't open until August, according to the ranger district.
It has been many years (1976) but I did a tour in a CJ5 I would like to repeat. From the Front Range I went to Como and took Boreas Pass (not 4-wheel) to Breckenridge. Then down to Alma for Mosquito. Camped in Leadville. Then Hagerman to Basalt and camped near Aspen. Then drove down to Marble and took Schofield to Crested Butte and spent the night in Gunnison. Then on to the Alpine Tunnel and Hancock Pass to St. Elmo.
I have done a lot of passes since then and repeated some of these, but never in a row like I did then.