I think that you and a lot of other people in this thread are kind of narrowly focused. The (many) reasons for the "rise of the West" are complex, multifaceted, and feed into each other in a virtuous cycle. Talking about how the Muslims just need to adopt Capitalism is simplistic IMO. For one example, it doesn't fix how inherently crappy the land in much of the Middle East had become over the centuries while agricultural innovations and New World crops caused European land to get better and better. Furthermore, I am doubtful of the 3 ways you list to encourage Capitalism. The development of Capitalism throughout the decades is another complex and multifaceted process intimately tied to the European setting. For example, a major fuel for the rise of merchant power and economics was colonialism and the urgent need to trade with the East. This doesn't work for states in the Islamic World because they're in a very different situation socially and geographically and economically and etc. I think that these kinds of broad structural changes to the course of history is precisely what AH is very ill-suited for.
Thus, I think talking about how the rest of the world can "keep pace" with Europe is a bit of a lost cause. A more fruitful endeavor IMO would be to have a POD late in the game when the other states realize how outmatched they are. For example, the Ottomans were at there lowest point around the turn of the 19th century and Napoleon was a wake up call. There were some excellent reform efforts despite the large number of inherent and imposed handicaps. Have them win the 1877 war and I think there's a very convincing case to be made that they could thrive.
I do not think that it is a narrow view that I am purporting, I am speaking on era's far before colonialism an ways for the Arab to advance in a way that in the end puts them in a more equitable playing field with Europe. No state will benefit from the same factors that Europe did, obviously, however, the development of a rigid merchant class and individualism in the Arab world would start the move to secularism and the eventual values that truly set Europe apart from the world.
Further, I disagree with your assessment in colonial influences on the growth and creation of capitalism and toward the eventual move to the need of Capital over mysticism, which is what Europe brought to the forefront which the world across lacked. For instance, we start to see due to decentralization inherent in European systems of feudalism lead to the creation of the Hanseatic League, Novgorod, Venice, Genoa, etc... Merchant classes who operated less and less without complete control by the religious authority or the government. All these started long before colonialism, again due to a progression of feudalism into capitalism, dialectical materialism dictates this progression as did the ideas of Marx and later thinkers who connected the creation of capitalism to a move from the nature of feudalism to the creation of a new class, being self made merchants in opposition to the previous power, nobility.
Arabs missed out on this progression, it started as a monolithic mega entity with borders too large to spread effectively and a state large and imposing, which by the Abbasid period began removing individual rights and curtailing merchant classes previously common amongst the Jahil period. In the short run, Arabs benefited from this and dominated the landscape but overtime the system of monolithic statesmanship and the slow erosion of voluntary market practices made it to where eventually the Europeans who while suffered short term, benefitted in the long run, very interesting indeed.
In terms of land value brought up, it depends on the area. Much of this is essentially caused by modern perceptions combined with climate change, the land value and population base prior to the late Abbasid period was not particularly small and not was desertification near the level today with rapid climate change. Egypt for instance was extremely rich before it was mismanaged by monolithic mega states such as the Ayyuib, Abbasid, Banu Hilali, etc.. Yes major cities where built in Fustat-Qahirah, but usually at the cost of farmland and agrarian growth, Europe did not see this due to feudalism and the decentralized nature of their system. Give this to the Arab world and desertification will not occur at such a level and likely the areas will sustain more in comparison. Also, the evidence of Roman censuses has Egypt at a very large populace and large crop production. As well, butterfly the Abbasid's silly ruling and it is foreseeable for Iraq to remain a large population base, albeit not like France, but that is not necessary.