The last time I played Warframe, I had completed the Sacrifice and nothing new was coming out. Haven't done the New War yet, so if there are new big players or powerups revealed in there, I don't know about them.
The Warframe setting seems to be vastly more powerful than NuBSG's ships in terms of raw firepower. Warframe ships also have shields. Lastly, Grinner and Corpus fleets are humongous compared to the size of the Colonial military, let alone just Galactica and Pegasus. And that's not getting into stuff like Grinner bordering parties or infested breeching the hull of a ship and tearing the crew apart. The colonial fleet's best chance is to head towards one of the relays, as those are the only safe spaces in the Warframe setting.
(Now that I think about it, is there any explanation why the Relays in Warframe haven't been destroyed by Grinner fleets/Corpus/Infested/Ancient Orokin automatons/the Sentients/whatever else is out there? Is it just the player Tenno, with some help from the Syndicates keeping these Relays protected?).
The fleet could integrate into the society of the relays and become powerful by producing and selling their version of FTL technology, which is ofcourse safer than trying to jump through the Void. Perhaps Galactica and Pegasus could be retrofitted with better weapons and shields and help out the Tenno in purging the system of the bad guy factions.