It’s really hard for me to recommend you change from the 243 for whitetail. But, I get that sometimes more bigger is more better, even if it’s not super practical. I’m still finishing up a 35 Whelen build myself.
If you want to keep your short action and get a medium bore thumper, go 338 Federal. (If you dont' mind new mags and swapping the bolt stop, then 35 Whelen). The 358 in a short barrel is going to be pretty slow. So is the 338, but slightly less so. Source your brass and dies before getting the barrel. There are far more practical choices (243, 308), but who cares? Build something different.
ETA: If you do go for a thumper in a lightweight Tikka, replacing at least the recoil pad if not the stock is highly recommended. My Whelen kicks aplenty and it weighs over 9 pounds in a Boyd's hardwood stock.