rockquarry, I too used bullseye powder for NRA bullseye shooting. Years back many old timers lauded the 3.5 grain load as the one to run. I ran with 4 grains for my Clark longslide.
When I had the chance I did some testing using a ransom rest with commercial #68 200 grain bullets that were inspected and sorted by weight. I found that the 3.5 Bullseye load grouped poorly at 50 yards, you could barely cover the group with your hand. I went to 3.6, 3.8 and then 4.0 grain load. In all cases accuracy improved as the load went up in grain weight. The 4.0 load was under 3", which may not seem great but that load had unweighed bullets. I meant to load some warmer, like 4.2 and higher but never got to do it.
I would suspect your 4.4 WST and 4.2 Titegroup similar or a little faster than the 4 grain bullseye load. If you have some bullseye try loading it incrementally higher, it may start to pull together for you as it did for me.