I have hiked, camped, climbed and fished in the upper rocky moutains. If you said you want solitude, I would definetly avoid Glacier. I use to think Yellowstone was the worst for crowds but I think Glacier now has them beat. You can have a great, relatively secluded, backcountry experience in Yellostone. However, you need to apply for a permit as there is a limited number and can be stiff competition for them.
I would also tell you to avoiod Glacier that early. Many of the good trails will not be snow and ice free until early July at best. Looks like they have been getting more snow lately so it is not uncommon for many of the trails not to open until late July. Lastly, the mosquitos will be bad then.
I might suggest some alternatives. It depends on how much you want solitude. An alternative to Glacier is Bob Marshall Wilderness. However, it does nto have the Alpine look and feel of Glacier. It does have a feature called the Chinese Wall as well as numerous lakes and streams for fishing.
I think the best alternative wouldbe the Bridger Wilderness in N.W. Wyoming about an hour from Yellowstone. It has the same look and feel as Glacier without near the crowds. Some areas, like teh Cirque of Towers, gets more pressure. If I was going to suggest one place in particular it would be the Green River Lakes area. Crowds are relatively light and has good access to day trips and extended climbs. Once you get away from major trailheads, good luck seeing anybody. Misquito's will still be ab issue then as well as some snow on higher elevation trails. Lastly, the fishing is good. Granted, it would be excellent the later you go.
