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What is the value of the 9 second SBF, how much is in that? Given that, a nice high budget for the engine and chassis, why not give plenty of love to the trans? I suggest a more modern trans, although I do have a rebuilt(not upgraded) C6 you could talk me out of.
I'd suggest thinking about a 6R80, the 1st gear is 4.17:1, and 6th gear is still 0.70:1, so plenty of strong gears. With no bands, it's stronger that almost all older stuff.
The hardest part is the cost, and the control system. It can be done without a $700+ adapter kit. The TC should cost about the same as a nice 4R70W unit or others. But the trans rebuild cost is a bit higher, you have to add at least the $600+ upgraded clutches, and a $600+ intermediate shaft. The 6R costs a good $300+ more just for the regular rebuild parts and solenoids. So the 6R can end up being easily $3500 plus the needed ring and pinion gear change and new driveshaft.
I'm plotting on a 6R swapped into my 98 Explorer, using a 2014 F150 PCM to run it and the SBF. I've just been browsing for drive by wire TB's, it will have to have that and the matching pedal, and some rewiring for the CC at the least. But the PCM control I have a plan that should work, for the cost of harnesses for the PCM, tuning, and work to the cross member etc. Without an adapter plate kit between the block and trans, it makes it a little shorter than other examples. You have to be willing to do without one bell housing bolt.

I'd suggest thinking about a 6R80, the 1st gear is 4.17:1, and 6th gear is still 0.70:1, so plenty of strong gears. With no bands, it's stronger that almost all older stuff.
The hardest part is the cost, and the control system. It can be done without a $700+ adapter kit. The TC should cost about the same as a nice 4R70W unit or others. But the trans rebuild cost is a bit higher, you have to add at least the $600+ upgraded clutches, and a $600+ intermediate shaft. The 6R costs a good $300+ more just for the regular rebuild parts and solenoids. So the 6R can end up being easily $3500 plus the needed ring and pinion gear change and new driveshaft.
I'm plotting on a 6R swapped into my 98 Explorer, using a 2014 F150 PCM to run it and the SBF. I've just been browsing for drive by wire TB's, it will have to have that and the matching pedal, and some rewiring for the CC at the least. But the PCM control I have a plan that should work, for the cost of harnesses for the PCM, tuning, and work to the cross member etc. Without an adapter plate kit between the block and trans, it makes it a little shorter than other examples. You have to be willing to do without one bell housing bolt.