I don't know how good your linkshells are, but you can absolutely finish a relic in the time left under the right circumstances. It took my LS around 17 days from the time we finished hamlets to the time we got our first Ifrit X win, and that included learning 17mins for the first time plus several off days in there. With experience though you can do a relic in 3-4 days no problem. Either way, there's enough time left under the right conditions.