What is the end goal or purpose of the rifle? Are you looking for a lightweight hunter or a heavier bench gun, or... ?
Precision shooting, bench and prone.
MDT has the ESS and LSS-XL both of which are available for your left-handed Tikka.
Of those two, the LSS-XL in lefty Tikka does not normally come with the fixed buttstock interface. The carbine interface is not ideal for precision as your options for an adjustable and stable stock are fairly limited (although MDT do offer a few options.)
Precision shooting, bench and prone.
I can understand the selection of carbine precision buttstocks is a bit limited, but I don't think it's fair to say its not ideal. We have released a few new options depending on your price point, and I love the pairing of the carbine interface with the SCS-Lite. Makes for a nice balanced rifle if you are using a factory contour heavy barrel in the 22" - 24" range.