No worries man. 44T to 4K looks like a pretty good mixup setup, I'll try to incorporate it while I'm playing next time. BT 8T will be good against sidestepping and those looking to counter BT P+K. Her moonsault seems to be the best choice in terms of the options you have on block and knockdown. On block, you'll be at advantage to continue pressure, and from knockdown, you can go for her reset to whatever.
A couple thoughts: I know BT 7p won't quite hit after 44f+p 4k, but I'm pretty sure 7pp will interrupt if they try something. So it might move you close enough to try BT 7k. Also haven't tried BT f+k or BT 2f+k, but those might not be the worst options. I think turning around by holding 9 to 9p from BT might work well too; even if they duck 9p they might still eat the knee. I'll see how this goes.
The 3k/hold 3p/throw mixup is very safe from the 4k; I'd use it liberally. BT p+k and BT 8f+p are awesome but they are reactable. Once they start expecting them the part where you just kind of duck for a second and throw them can be quite a surprise. On that subject, anyone know the absolutely fastest way to turn around from BT? It'd be kind of awesome to get this setup right into 44p. At +18 or so you'd think it'd be fast enough to work.
I've found FC 3P to be better for force teching then 8P.
Curious as to why? Preference for the immediate throw/mid mixup to the 46p/46f+p options? I haven't really tried this as a pseudo (I will) but I'm not sure if you're trying to throw why you wouldn't use 1p 6f+k? Slightly more damage and +9 is enough for most of the reasonable mid and throw mixups you might try. hold 3p seems to be kind of a bad compromise; it's not like it gives you enough frames to go for 8f+p or anything exotic. Suppose it might be better for 7k though.