I am left handed and own left handed bolt action rifles. The choice/selection used to be poor. Fortunately, things have greatly improved since the 1980s.

Focussing on controlled round feed - Mauser and pre 1964 type Winchester Mod 70 (& clones)there are rifles to suit just about everyone's pocket.

Mauser CRF

Zastava / Charles Daly are now offering / will soon a Mauser M98 in .375H&H. Barrelled actions and actions are also available. With this action length / bolt face, you could re-barrel to most DGR cartridges. they also make deer cartridge 30.06 & 7x57 length left hand actions.

Empire Rifles make a nice looking Mod 98 Standard action suitable for DGR and deer cartridges.

Win Mod 70 CRF & clones

Winchester / USRAC make their new classic in deer calibres plus with an action length suitable for .375H&Hmag. They used to advertise a .375H&H mag in left hand - Safari, but I could never find one. In the end, a purchased a .300Win Mag for the action. I am in the process of having built a 375 using a Williams one piece bottom metal, Shilen barrel. Present status - trying to sort out a stock.

Waffen Fabrik Hein make a nice rifle too. These are available in DG and deer calibres.

Dakota make a nice looking, in the classical style left hand rifle for both DG and deer.

I mention these makers because I think they represent the price end members for each group. After that, you are in the realms of custom actions / rifle makers. If you have to ask the price, you cannot afford it anyway territory.