I am trying to decide between adding Flash to the Motif with the Complete Orchestra Library or going the Integra route which is more expensive in the short term. [...]So If I add an Integra I will also need a Mixer for the Tyros and Integra so I can feed their output into the Motif A/D input.
I was quite disappointed with the DCP Complete Orchestra first, just bought it 3 weeks ago, some samples are incredibly bad (e.g. violins with only 1 sample for the entire key range, so that the sampled vibrato gets ridiculous). A few samples are very good. Eventually I found it is a useful library (Garritan GPO too) if you mix the samples with the Motif's factory samples, then in SOME cases it sounds even a bit more realistic than the Roland expansions. Mixing this with the Integra will nearly be the 'ne plus ultra'.
I think you don't need a mixer, you could use the Integra's audio input for the Tyros and then direct the joint signal to the Motif input.