Is it acceptable to ask for this leave just before or just after my
review? It almost seems like I am asking for too much, especially if I
end up having to negotiate my raise.
You can ask for leave any time you choose.
If your concern is that asking for this leave would impact your raise, then clearly you should ask after the annual review and raise process is complete. You know management at your company and hopefully this doesn't apply for you, but some managers would consider a 5-6 week absence as evidence that your role isn't really needed by the company very much.
Other than that, asking sooner is better for the company as it will give them a bit more time to prepare for your absence should your sabbatical be granted.
In my US locale, and in the companies where I have worked, asking for such an extensive leave after being with the company for only a year and with only a few months notice would be considered "too much".
On the other hand, in several companies where I worked it was common for people to "save up" vacation time for several years in order to use it on an extended trip back home (typically India or China for 3-4 weeks). But this was always agreed to years in advance.
It's unfortunate you didn't get an agreement for this leave during the hiring process a year ago particularly if this is something you would like to do repeatedly.