The issue I am having with bcrypt is that the module can't be imported into the Pythonista app on iOS, which is where I need to run my script. What else would you recommend similar to bcrypt that can generate a random salt, and has something like the checkpw() function built-in to quickly validate salted passwords?
If pbkdf2 is natively available, I'd use that before trying to roll your own bcrypt. When its work factors are sufficiently large, it's still a solid choice when bcrypt or scrypt aren't available, and using it directly is safer than trying to recreate something else by hand.
Not knowing more about your use case, a general recommendation: use pbkdf2 with a sufficiently large number of rounds to take about a half-second's worth of the upper end of the processor throughput of your target devices. This keeps the UX within tolerable wait times while still providing reasonable resistance to offline attack.
I'd also recommend randomizing that number of rounds slightly over a range (like a thousand). For example, if you settled on 200,000 as having an acceptable 500ms delay, I'd randomly pick a value between 200,000 to 202,000 (or something like that) - whatever is needed to ensure that most users will have different rounds from each other (assuming that all user passwords might be aggregated into a single location that could be compromised and the hashes stolen). This is because some of the newer "associative" / "correlation" attacks only work well against a large set of hashes when all of the cost factors across that set of hashes are the same.
Long term, also be sure that your code easily accepts a variable floor and ceiling for the number of rounds, so you can choose to increase your number of rounds over time as processors advance. (You could even get fancy and dynamically calculate the range of rounds based on the processor that the password is being created on, so that it's future ready without any additional intervention.)
What hashing algorithms would you recommend I use in Python3 that can generate a random salt, other than bcrypt?