I hiked the length of the Lakeshore Trail 6 -7 years ago. My son and I hiked in from the tunnel to Forney Creek the first day and fished it that evening and the next morning. He headed back out and I continued on. I was only doing 6 to 8 miles a day and fishing here and there in the evenings along the way. This was before they cut the new trail from Hazel to Eagle. The old route took you up Hazel to 84, then across Jenkins Ridge to Eagle. That was my first of several trips to Hazel. As well as I recall, it took me about 3 days to get to 84. Some of the trail was flat along the lakeshore, but there seemed to be endless trips up and down little finger ridges. I'm sure it could be done in a day, but it would be one tough day. The trip from the dam to 84 could be made much easier in one day, especially now that you don't have to go over Jenkins Ridge.
I think the question is going to come down to how much money do you have to spend and would you rather hike or fish. To take the shuttle over from the dam will cost you $50 a head but save you 3/4 of a day hiking. If you're determined to hike it, come in from the dam.
Site 84 is about 4 miles up the trail. The hike is on an old road bed and probably has no more than 500 feet of elevation gain. It just might be one of the nicest camp sites in the Park. 83 is about a mile further, not as pretty, also a horse camp, but there are several nice tent sites over a small ridge, away from where the horses stay. If you're doing a Monday - Friday trip, that will really decrease your chance of sharing the site with horses. I've never stayed at 82, but it's also a pretty site. 84 and 83 have a spring fed water source - 82 has only the creek for a water source. (I hate pumping water.) The hike from 83 to 82 is about 3 miles, but it's not an easy 3.
My personal preference is 83. It's an easier hike with a good water source. You can day trip on up to 82 and beyond much easier than lugging a full back pack up there. Sounds like you've done your homework in wanting to spend a day on Bone Valley. It's only a mile up the trail to the Hall Cabin (see my avitar), but don't be afraid to bushwack your way further up the creek.
From what I've seen, the most pressure is from the mouth up to 85. Like highpockets said, the further up you go, the fewer people you will see. We also try to do our trips there during the week to avoid the crowds. One year we saw at least 20 to 30 folks at 86 on a guided trip out of Charlotte and another 10 or 15 at 85. That was on a Friday and thank goodness, we were on our way out.
Lastly, I'd say the later in May, the better. I say this because I usually wade wet so I don't have to haul waders in. The water will be a little chilly first thing in the morning, but you'll get used to it soon. Avoid the Memorial Day weekend.