My wife and I live in Reading. We have been on the Bartrum Trail a number of times.
We get on outside of Hamburg, PA at the old de-silting basin. You can look at the trail on something like MapQuest. The trail still shows as the old rail line.
One mile long section has been built from Route 895 just east of Auburn, PA. There is no trail from Route 895 to Landingville. Their is about a mile of trail at Landingville that goes nowhere.

There are plans to complete the trail from Hamburg to Route 895 outside of Auburn. That requires decking an old railroad bridge that crosses the Schuylkill River just South of Auburn. The landowner on the Auburn side of the river refused to give any of his ground for the trail. He has horses and does not want public access to his property.
I have talked to people who have gone from Hamburg to Schuylkill Haven using this trail. Starting out at Hamburg. When you get to the bridge there is a large fence blocking the trail. So they cut off the trail over Auburn Fish and Game property to a paved road. Then used the paved road to work their way into Auburn. On the East side of the Schuylkill River on Route 895 you take a road that runs back behind a large PVC film and sheeting plant. Omnova. That road will take you up to Landingville then a short run on another road takes you into Schuylkill Haven. I don't know of any roads that you could use to go from Schuylkill Haven to Pottsville other than Route 61. There is Route 901 that runs from Cressona, outside of Schuylkill Haven up to Route 209 which then takes you into Pottsville. None of these roads have shoulders wide enough to safely ride on. We never see any road bikes on them. Very hilly and a lot of sharp turns.

This Bartram Trail is stone dust paved. Some sections get a little rough due to the amount of use by horses. The scenery is real nice. Almost all of the land along the trail is state game land.

The section from Hamburg down into Reading has been looked at. Trouble is that the old rail line is still in use. So the future plans call for a lot of back road sections. Just South of Hamburg you could pick up the back roads off Route 61 into what is known as 5 Locks on the old canal. Back road into Shoemakersville and down into Leesport. But then back onto Route 61.

You might want to look at the PA Bike Route maps to see if there are any that would fit into your ride plan. We have seen large numbers of bicyclers doing East to West rides on back roads in Schuylkill County. I think that Route 73 from its intersection with Route 61 would take you down into Skippack via the Oley Valley. That you would pick up near Leesport than trough Blandon and down into Oley and then down to Boyertown. Most of Route 73 has nice wide shoulders.