Saweeth and the Lower Great Range via Alfred E. Weld Trail
My recommendation ( for what it's worth) is to ascend to the Saweeth/Pyramid col via the AMR Lake Road and the Alfred E. Weld trail. The road is tedious (at best), but nevertheless provides access to what many consider the best (ATIS) hiking trails in the High Peaks.
Your hike presents a serious challenge, but it has been done in one long, tiring, but extremely rewarding day. Be advised that after leaving the middle section of the Weld trail there is no water on this route until your descent and therefore carrying as much water as you possibly can is strongly encouraged.
After reaching the Sawteeth/Pyramid col on the Weld Trail, the RT route to Sawteeth's summit is conservatively an hour. After returning to the col, the ascent to Pyramid Peak is quite steep in sections and takes about 45 lung-dusting minutes to reach.
However, Pyramid Peak, at 4595', IMHO, is the most incredible panoramic view in the entire Adirondack Park. But don't take my word for it. Tony Goodwin, editor of the ADK High Peaks Region Guide states that Pyramid, " offers the single most spectacular view in the Adirondacks."
My log record shows a 20-minute descent from Pyramid/ascent to Gothics, followed by 45-minutes to Armstrong, 60-minutes to UWJ, 45-minutes to WJ col and a RT to LWJ of 35-minutes.
Be advised that there is only one contingency trail (Beaver Meadow Falls Trail) in the col between Gothics and Armstrong. Once you decide to continue on the Range Trail to Armstrong, there are no other emergency or back-up routes until you reach the WJ col.
From the WJ col, it is nearly all descent on the Wedge Brook Trail, West River Trail and Canyon Bridge to the Gate and eventually the road leading to public parking on Rt. 73. The descent time from WJ col is about 2.5 hours on "Gumby" legs to the Gate.
Plan on a conservative estimate of 12 hours to complete the loop. I would advise more in order to be able to linger on these rugged summits. It is, as stated previously, an extreme challenge, but an unforgettable one given the right weather to enjoy the summits.
IMO, on a good weather day, there are very few hikes that compare to this. Enjoy!