Alan -
When you get that screetch it's caused by electrical feedback. It's exactly the same thing that happens when a microphone feeds back except that it's happening between the effects boxes instead of through the air. There's too much treble gain when you have the high band boost going, whether on the SF-2 or F-1X.
Part of the reason that this comes up is that devices like the SF-2 have a really wide frequency range. It's much wider than you will hear or use, but when you set the high band eq to boost the highs, it's probably doing so happily and signficantly past 10KHz. The big boost in the inaudible treble may be overdriving something later in the signal path.
The other problem here is that the input and output impedances may not be properly matched. When they're not matched correctly, some of the output signal will reflect back which can have weird effects on both devices.
So, I'd debug this stepwise and report back. First, I would try just the pedal board in the effects loop, play with pedal settings and turn the F-1X treble boost to see if the problem is still there. Then, take the pedal board out of the effects loop and try the SF-2 there and see whether you're getting the screech. It may work with either, or you might identify the problem.
I think it's much more likely that the pedalboard will be problematic. Traditionally, the effects loop level is much higher than instrument level which is one problem (it may make using a dynamic filter challenging). The other problem is that effects loops are designed with medium impedance, but stompboxes were designed for the higher impedance of the instrument inputs - that will trigger these sorts of feedback problems.
One thing that should work would be to move the pedalboard even earlier in the signal chain. In this case, you'd go
1) bass to the DS-5R
2) DS-5R mono out to tuner in
3) tuner out to the first device in your pedal board
4) through the pedal chain
5) output from the last device in the pedal chain to the SPB-8C left pedal in
6) left output of SPB-8C to F-1X front panel in
7) SF-2 living in the F-1X effects loop

biamp outs to the amplifier in
The SPB-8C isn't doing much in the signal chain (you could have went from the last pedal to the F-1X), but it is containing and powering the pedals which is a good thing.
This would present the pedals with the normal environment that they expect to see, which should solve the feedback problem.
Your terminology was a little funny a few posts back. You referred to the Boss trem pedal as being the last in the chain. I think it must be the first in the signal chain, otherwise you probably wouldn't be hearing anything. The bass input is fed to the trem first, then from the trem to the envelope filter, right? This is just wording in a complicated setup!
David Fung