So I know that being the receiver of interest payments is not allowed in Islam. That said, is paying interest allowed? For example, would a Muslim be able to buy a home with a loan that charges interest, or would they have to wait until they could pay the full value?
The answer of your main question "Is paying interest allowed?" is no. Paying interest is not allowed.
If you pay interest, you are helping the recievers of the interest. You are encouraging them to recieve more interest. According to the Al-Quran, helping others to commit sin is prohibited.
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allah. Verily, Allah is Severe in punishment” (Surah Al-Maa’idah, 5:2).
Well, this would take a fully fledged Islamic finance initiative. Some Western banks are looking at this seriously where, for example, they part own a property and charge rent on this. This gets round the prohibition on interest.
Given that one is living in the West, one must do what is best given the circumstances. Islam is a rational religion and not an irrational one. If it turns that keeping to a prohibition is simply not possible then one is allowed to bend the rules of sharia somewhat. Or better put - sharia has allowances for difficult circumstances.