As you mention, this is something we have real-world evidence for
There's some good real-world examples in our own evolutionary history. There are two known interbreeding 'events' between homo sapiens and other related hominins, and I've heard of evidence of at least one more interbreeding event with an unknown 'ghost population'.
There's genetic evidence that sapiens interbred with neanderthals in Europe, enough to contribute nearly 1.5-2.1% of the DNA of all humans outside of Africa. Our common ancestor was Homo heidelbergensis, which we diverged from about 300,000 years ago and neanderthals did about 240,000 years ago. The earliest suspected interbreeding period was around 110,000 years ago, and the latest around 47,000 years ago. So we have a potential window of 190,000 years of divergence, after which interbreeding was evidently still possible.
However, there has been no evidence of neanderthal mitochondrial DNA found in sapiens population. This suggests that while male-neanderthal/female-sapiens parings produced fertile offspring, the offspring of female-neanderthal/male-sapiens parings were infertile. This could also be suggestive of a very low rate of interbreeding between the two (sub)species, but might indicate that sapiens and neanderthals were nearing the point at which they couldn't interbreed.
There is also genetic evidence of an interbreeding event between sapiens and denisovans in Asia, which contributes between 3-6% of of the DNA of Melanesians and aboriginal Australians (and a lower percentage in Southeast Asians, including Tibetans). The ancestry of denisovans is less clear than sapiens or neanderthals due to the limited number of finds, but best guesses suggest they're more closely related to neanderthals and split from them around 160,000 years ago (possibly interbreeding with another, unknown archaic human population).
Current estimates put the interbreeding event between sapiens and denisovans at around 44000-54000 years ago. If denisovans are derived from neanderthals, that would put a window of around 246,000 years, after which interbreeding was still possible.
Similarly to neanderthals, there is evidence that sapiens-denisovan pairings weren't always fertile. There are large parts of modern human genomes that are devoid of any denisovan DNA, the location of which could be explained by male hybrids being infertile. This would also suggest that humans and denisovans were approaching the point at which they could no longer interbreed. However, due to the scarcity of denisovan finds there are a lot of questions still unanswered.
To find out the level of morphological differences you're likely to be able to support via natural genetic divergence you can look at the comparisons between sapiens, neanderthals and denisovans. As a starter for ten the latter two were more robust than sapiens with more pronounced brow ridges, and denisovans had different dentition.
Another approach: artificial breeding
If you're looking for greater morphological differences, but retaining the ability to interbreed then you could look at dogs. It would take some creative circumstances, but perhaps all your various breeds of hominids were selectively bred by a historical (and now absent) population. This could conceivably allow for some very distinctive physical differences with minimal genetic divergence.
A cursory google indicates that there might be some concerns around the ability of some very isolated dog breeds to produce fertile offspring, but the general consensus is that even dachshunds and great danes can produce fertile offspring. From here, we're talking about purely mechanical problems with the ability to produce offspring (I wouldn't want to see a non-giant try to give birth to a giant-hybrid).