In other words Nagasaki and Hiroshima were not randomly chosen, but rather they were chosen for their geographic potential for testing a nuclear device on a populated city centre.

The motivation for nuking Nagasaki might have been dubious, but it definitely wasn't for Hiroshima. Hiroshima was the location of the HQ and distribution hub for the Japanese Second General Army; the military force responsible for the entire defense of southern Japan. Hiroshima being wiped off the map was a HUGE bitch slap to Japanese defensive preparations. Of the people killed, ~20,000 were uniformed soldiers, and among those was almost the entire top brass for the JSGA. The thousands of soldiers that survived were to traumatized to be of any use.

Needless to say, with the Soviets closing in,

This is really disingenuous. The Soviets were closing in on the Japanese forces left on the mainland, not Japan itself. The Soviets had dick for naval assets in the Pacific. Not even close to enough to form an invasion fleet. The Japanese were very much aware of this, which is why they were continuously moving troops from the north to the south all the way to the end of the war in preparation for a US assault, not a Soviet one. There was zero plans to include the USSR in preparations for Operation Downfall.

and Truman having no interest in splitting up Japan, meant that that was the primary reason for dropping the bombs in the first place.

The primary reason by far was to avoid committing to a ground invasion of Japan, which would have made D-Day look like a cakewalk. It would have been the largest naval and amphibious operation in the history of mankind. Japan is like a natural fortress. Defenders know almost exactly where an invader will be forced to land just by knowing the direction they are coming from. The Japanese army was already dug in where the beachhead was supposed to be, and 90,000 men were moving to reinforce the position. For a time there was seriously deliberation on whether to use the nukes on the defenses due to how ingrained they were predicted to be.

Contemporary casualty predictions for Operation Downfall ranged from half a million to over a million for the allies, and millions for the Japanese. The US government was so certain of the brutality of the campaign that an order was made for 500,000 Purple Hearts in preparation. To this day we are still going through that order. Only a couple of small batches have been made since in order to ensure production is still possible. Almost all the casualties from Korea through the War on Terror have utilized the medals from the order, and there's still ~60,000 left.

Worries about Soviet reprisal demands probably played a roll in the decisions made at the end by the US government, but I am certain that by far the biggest factor was the drive to spare America losing a massive swath of its young men in addition to the losses already suffered.