"...looking to spend around the 800 mark..." Hi. You won't normally get a Tikka with sights for that much. Goble's(not the least expensive shop on the planet, but they're close to you.) price list indicates $807.50 for a Tikka T3 Synthetic. Goes up from there. However, they are listing a left hand, .270, T3 Synthetic, on their Used Rifle page, at $695.00 though. Says it's new, but it's at their Tillsonburg store. No sights. It'd be worth a look, but I wouldn't wait too long.
They want $649.95 for a Remington SPS, no sights. A Savage 110 GLXP3 Package(comes with a low end scope) runs $752.50. It's very hard to beat a Savage.
All new firearms require a trigger job. Frivolous U.S. law suits, but it's nothing new.
Don't discount a used rifle. It takes a great deal of abuse to damage a modern hunting rifle. You might find a used .270 with a higher end scope on the used rifle shelf. Nothing on Goble's site.