Timing of the admixture is measurable by linkage disequilibrium--or the length of genomic segments that come from one population or another.
Admixture with Neanderthals at a minimum by about 50-60K years ago. This date is skewed young as their is good evidence that more than one admixture event took place.
Denisovan age range is indeed 44-54K years ago. However, this again could be skewed to the young end as it is possible that introgression took place up to 3 different times.
Did I misunderstand your hypothesis and that humans emerged out of Australia and Africa after Toba? I was fairly certain your theory was just Australia.
An australian origin has issues for multiple reasons--the high genomic diversity in Africa (generally a sign of depth of time for a population), the fact that ALL mtDNA and Y chromosomal data roots in Africa not Australia based on phylo-geographical studies.
"All Australian lineages are confirmed to fall within the mitochondrial founder branches M and N and the Y chromosomal founders C and F, which are associated with the exodus of modern humans from Africa ≈50–70,000 years ago. The analysis reveals no evidence for any archaic maternal or paternal lineages in Australians, despite some suggestively robust features in the Australian fossil record, thus weakening the argument for continuity with any earlier Homo erectus populations in Southeast Asia." [www.pnas.org]
All extant human populations with deep maternal ancestry in Eurasia carry mtDNA lineages that fall within a single haplogroup, L3- this is firmly rooted in Africa-no where else
Autosomal microsatellite and SNP coalescence times are, negatively correlated with distance from Africa, suggesting a single dispersal and serial founder effects going east. Also you have a general decrease in population diversity as one gets further from Africa-demonstrating serial founder effects.
The genetic and archaeological data is rather clear on this. The dates may move a bit up and down.
Their is less and less doubt that AMH made it out of Africa and perhaps as far as China as much as 100K years ago. But these early migrants have left no genetic legacy on any modern population tested so far. Everything, genetically speaking, root phylogeny wise into africa.
This may change but that is where the vast majority of the data now stands.