The TSR-8 wouldn't be my first choice for tape saturation, the 80-8 would probably have been a better bet. The TSR-8 is a really nice machine, but it was intended as a cheaper alternative to a digital recorder so they put a lot of effort into making the response flat. In other words it might be a bit too clean for what you're trying to do.
For this I'd definitely run the machine with the DBX turned off, since overloading the DBX will cause tracking errors instead of saturation.
As it happens, I've also purchased a Fostex A8LR which is a much older machine, running 1/4" tape at 7.5IPS so I'm hoping between the two machines I should be able to get the desired levels of tape saturation. For me though, it's actually more about adding a sense of 'realism' to my recordings. Of course, the analogue pre-amps and EQ from my desk achieve a lot of that, but most of my drums are MIDI created in Logic, so sending those out to a tape recorder should really make them sound much more real. The cool thing about the Fostex is that one does have 3 heads, so I could use it as a tape echo as well. It was quite a bargain (£108), but the seller says channel 1 doesn't record (it registers input signal and plays back, just doesn't record) - hopefully it'll be a relatively easy fix, but if not, I've still potentially got 7 more tracks of grit to play with!