I read your post. You have a lot of detail in there. As you mention, the IISS publication is not publicly available. We can't scrutinise how they came up with their numbers or if their sources are recent.

The 169.5k is not far off your 180k. Wikipedia may have combined the numbers for compulsory service and 'rapid reaction' reserves. So that is 465k vs. 590k.

Wikipedia also includes reserves for Iran and Turkey but I considered them less relevant, so I didn't include them.

You might be underestimating Iran's and Turkey's military. Both countries have modern tanks. Iran has the Karrar and Turkey has the Altay

Turkey's air force has some new refurbished F-16s. Iran's air force seems close to non-existent.