VOY finding an ancient teleport machine would be no more contrived than Crichton receiving wormhole information in his mind from a random encounter with aliens or the Stargate SG-1 folks finding out that the secret superweapons they search for were on Earth all along.
TNG and DS9 didn't stay in the confines of existing elements of Trek when they created the Borg and the Dominion. They simply added new elements. VOY would just use their existing psychics and such in a way that the 8472 become their weapon against the Borg.
When DS9 did the Dominion War they had the entire Trekverse to play with, and lots of cannon fodder to sacrifice to the Dominion. It also didn't cost much since the only new designs they had to make were the Dominion ones, the Breen and the Defiant. Everything else was recycled from TNG and FC. VOY didn't have any cannon fodder to sacrifice, they were always just one tiny insignificant vessel, and their enemies were far stronger and superior to the Dominion. The 8472 were too costly to use as well.
The BSG folk had the excuse that they only had one warship and too many unarmed vessels to risk a battle. Once they had the Pegasus they started blasting the Cylons to scrap (until the reset button destroyed it). VOY was an armed vessel so running from everything would make them cowards.
Kirk and Picard never ran, they always triumphed over their foes.
Evasion never works with the Borg anyways, they couldn't evade them in Q Who? or BOBW. They only answer is to destroy them.