To get to the Mons hut the "proper" way you go a fair ways north along the rim of the canyon to bypass the cliff bands through easier slopes. It should fairly easy to tell where to go in daylight. Once above the major cliff band go back SW to reach the hut. I approached the hut straight on left of the waterfall and was able to break through the cliffbands on easy but loose ledges. This would probably save some time if you find an easy way though and don't mind some looseness.
On the glacier the route is pretty obvious to get to the East end. Stay high and you avoid most crevasse issues without loosing too much elevataion. Once you are closer to Forbes and where the ridge wraps around the couloir is on your left. It is the tall skinny one that goes up left of the tower. The middle was bare a week ago but was not an issue. (On the picture below, the left land is the Rosita/Forbes col and the right line leads to the bivi col and South West Col alternate route described later)
If you go up snow slopes right of this you end on a ridgeline isolated as the Rosita ridge splits in two in this area. Once at the top of the col you have a few options. Drop down onto the glacier below, or traverse steep snow above the schrund towards Forbes. My party opted to traverse but it was fairly steep (60º?) and exposed above the schrund. If you try to stick to the ridgeline you get cliffed out above the South Glacier Col route. - See next paragraph
The alternate route is to head to the col to the right just before the Rosita couloir to GR 032448 at approx 10,000 ft. My party and a party before us bivied here at the col to make a short ascent day. From the bivi site if you scramble up the ridge to the North you get a pretty good picture of what the area looks like. There is a tarn about 50m south of the col on the ridgeline for water. From here you can traverse on the right (south) side of the peak between you and Forbes. Go towards Forbes on a rock ledge and countour around (2 cairns) to rach the snow slope on easy but loose ground.
Once you gain the SW Forbes glacier go up towards the Rosita/Forbes ridge and climb through the middle (lowest) col on slopes of about 35º. The rest is straight forward.
There is still lots of snow in the area. I did the Lyelle traverse last year mid August and there is definately better coverage this year. Lyelle 1-3 are pretty easy. Lyelle 4 is a fun ridgeline. At the top of 4 there is some loose ridgework to do getting around some small towers. I think we went around most of them on the right. Lyelle 5 ridge is a really fun scramble. The descent towards the hut is on snow at first but you can avoid the majority of the snow on the rocks on the right, which is good after the sun has been heating up the slopes all day!
Hope this gets to you in time. Good luck!