Are the profits from conventional banks permissible in a non-Muslim country, given the absence of alternative employment opportunities in one's home country, and the inability of Islamic banks to provide a suitable return due to their dealings with conventional banks?

It is impermissible to take usurious interest except in cases of dire necessity, and your situation is not one of them. You must dispose of these interest earnings by spending them on the welfare of Muslims, and withdraw your money from the usurious bank, depositing it instead in Islamic banks. Your transactions with the usurious bank are forbidden, whereas transactions in Islamic banks are permissible. You can serve Islam through da'wah (inviting to Islam) and benefiting Muslims. You can also seek guidance from people of knowledge and righteousness to direct you to the best forms of ongoing charity (sadaqah jariyah).