Give the businesses Marrakai mentioned and enquire about doubles with them.
As a rule if you want a rifle in .375 calibre or above you will be very lucky to find a "Nitro" rifle under $5000 and possibly multiples of this, new or second hand. A new Pedersoli double in .45/70 is $4950, but personally I wouldn't go for a .45/70 for buffalo. Would be a fun rifle though.
The Baikal you mentioned is an under and over I would think. I saw one advertised for A$800 this month. A side by side Baikal is to come out sooner or later and will cost about $2000 new (from reports).
A smaller calibre double would be great pig medicine too and good fun to start with if the others are too highly priced. Often they can be priced a little lower, sometimes not.
PS We do have bolt action shooters here too
-------------------- John aka NitroX
...
Govt get out of our lives NOW!
"I love the smell of cordite in the morning."
"A Sharp spear needs no polish"